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Journal articles on the topic 'Fully nonlinear PDE'

Author: Grafiati

Published: 9 March 2023

Last updated: 10 March 2023

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1

Sirakov, Boyan. "Solvability of Uniformly Elliptic Fully Nonlinear PDE." Archive for Rational Mechanics and Analysis 195, no. 2 (2009): 579–607. http://dx.doi.org/10.1007/s00205-009-0218-9.

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2

Lions, Pierre-Louis, and Panagiotis E. Souganidis. "Fully nonlinear stochastic pde with semilinear stochastic dependence." Comptes Rendus de l'Académie des Sciences - Series I - Mathematics 331, no. 8 (2000): 617–24. http://dx.doi.org/10.1016/s0764-4442(00)00583-8.

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3

Wei-an, Liu, and Lu Gang. "Viscosity solutions of fully nonlinear functional parabolic PDE." International Journal of Mathematics and Mathematical Sciences 2005, no. 22 (2005): 3539–50. http://dx.doi.org/10.1155/ijmms.2005.3539.

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By the technique of coupled solutions, the notion of viscosity solutions is extended to fully nonlinear retarded parabolic equations. Such equations involve many models arising from optimal control theory, economy and finance, biology, and so forth. The comparison principle is shown. Then the existence and uniqueness are established by the fixed point theory.

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4

Wang, Falei. "Comparison Theorem for Nonlinear Path-Dependent Partial Differential Equations." Abstract and Applied Analysis 2014 (2014): 1–5. http://dx.doi.org/10.1155/2014/968093.

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We introduce a type of fully nonlinear path-dependent (parabolic) partial differential equation (PDE) in which the pathωton an interval [0,t] becomes the basic variable in the place of classical variablest,x∈[0,T]×ℝd. Then we study the comparison theorem of fully nonlinear PPDE and give some of its applications.

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5

Ikoma, Norihisa, and Hitoshi Ishii. "Eigenvalue problem for fully nonlinear second-order elliptic PDE on balls." Annales de l'Institut Henri Poincare (C) Non Linear Analysis 29, no. 5 (2012): 783–812. http://dx.doi.org/10.1016/j.anihpc.2012.04.004.

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6

Katzourakis, Nikos. "Generalised solutions for fully nonlinear PDE systems and existence–uniqueness theorems." Journal of Differential Equations 263, no. 1 (2017): 641–86. http://dx.doi.org/10.1016/j.jde.2017.02.048.

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7

Wang, Zhi Yu. "Finite Strain Analysis of Crack Tip Fields in Yeoh-Model-Based Rubber-Like Materials which Are Loaded in Plane Stress." Applied Mechanics and Materials 127 (October 2011): 477–83. http://dx.doi.org/10.4028/www.scientific.net/amm.127.477.

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The dominant asymptotic stress feild near the tip of a Mode-I crack of Yeoh-model-based rubber-like materials is determined. The analysis bases on the fully nonlinear equilibrium theory of incompressible hyperelastic solids. First, The nonlinear PDE (partial differential equation) governig the leading behavior of y2 is transformed to a linear PDE. Then the linear PDE is solved and the solution of y2 is obtained. With the solution of y2 and boundery conditions the numerical solution of y1 is obtained,too.Finally,the analysis solution in polar coordinate of the first Kirchhoff Stress in plane st

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8

Zhang, Jianfeng, and Jia Zhuo. "Monotone schemes for fully nonlinear parabolic path dependent PDEs." Journal of Financial Engineering 01, no. 01 (2014): 1450005. http://dx.doi.org/10.1142/s2345768614500056.

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In this paper, we extend the results of the seminal work Barles and Souganidis (1991) to path dependent case. Based on the viscosity theory of path dependent PDEs, developed by Ekren et al. (2012a, 2012b, 2014a and 2014b), we show that a monotone scheme converges to the unique viscosity solution of the (fully nonlinear) parabolic path dependent PDE. An example of such monotone scheme is proposed. Moreover, in the case that the solution is smooth enough, we obtain the rate of convergence of our scheme.

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9

Panayotounakos, D. E., and K. P. Zafeiropoulos. "General solutions of the nonlinear PDEs governing the erosion kinetics." Mathematical Problems in Engineering 8, no. 1 (2002): 69–85. http://dx.doi.org/10.1080/10241230211379.

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We present the construction of the general solutions concerning the one-dimensional (1D) fully dynamic nonlinear partial differential equations (PDEs), for the erosion kinetics. After an uncoupling procedure of the above mentioned equations a second–order nonlinear PDE of the Monge type governing the porosity is derived, the general solution of which is constructed in the sense that a full complement of arbitrary functions (as many as the order) is introduced. Afterwards, we specify the above solution according to convenient initial conditions.

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10

Ayanbayev, Birzhan, and Nikos Katzourakis. "On the Inverse Source Identification Problem in $L^{\infty }$ for Fully Nonlinear Elliptic PDE." Vietnam Journal of Mathematics 49, no. 3 (2021): 815–29. http://dx.doi.org/10.1007/s10013-021-00515-6.

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AbstractIn this paper we generalise the results proved in N. Katzourakis (SIAM J. Math. Anal. 51, 1349–1370, 2019) by studying the ill-posed problem of identifying the source of a fully nonlinear elliptic equation. We assume Dirichlet data and some partial noisy information for the solution on a compact set through a fully nonlinear observation operator. We deal with the highly nonlinear nonconvex nature of the problem and the lack of weak continuity by introducing a two-parameter Tykhonov regularisation with a higher order L2 “viscosity term” for the $L^{\infty }$ L ∞ minimisation problem whi

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11

KOIKE, Shigeaki, and Andrzej ŚWIĘCH. "Weak Harnack inequality for fully nonlinear uniformly elliptic PDE with unbounded ingredients." Journal of the Mathematical Society of Japan 61, no. 3 (2009): 723–55. http://dx.doi.org/10.2969/jmsj/06130723.

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12

Ikoma, Norihisa, and Hitoshi Ishii. "Eigenvalue problem for fully nonlinear second-order elliptic PDE on balls, II." Bulletin of Mathematical Sciences 5, no. 3 (2015): 451–510. http://dx.doi.org/10.1007/s13373-015-0071-0.

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13

Barles, G., and Jérôme Busca. "EXISTENCE AND COMPARISON RESULTS FOR FULLY NONLINEAR DEGENERATE ELLIPTIC EQUATIONS WITHOUT ZEROTH-ORDER TERM1*." Communications in Partial Differential Equations 26, no. 11-12 (2001): 2323–37. http://dx.doi.org/10.1081/pde-100107824.

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14

Bertens, M. W. M. C., M. J. H. Anthonissen, W. L. IJzerman, and J. H. M. ten Thije Boonkkamp. "Design of optical surfaces conform the hyperbolic Monge-Ampère equation." EPJ Web of Conferences 266 (2022): 02003. http://dx.doi.org/10.1051/epjconf/202226602003.

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We present a method for designing freeform optical surfaces for illumination optics. By the laws of reflection, refraction and conservation of energy, a fully nonlinear PDE, the Monge-Ampere equation, is derived for the optical surface. By the edge ray principle a transport boundary condition is obtained. We solve the hyperbolic variant of the PDE using a least-squares method, resulting in optical saddle surfaces for a parallel source and far-field target.

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15

Safdari, Mohammad. "Double obstacle problems and fully nonlinear PDE with non-strictly convex gradient constraints." Journal of Differential Equations 278 (March 2021): 358–92. http://dx.doi.org/10.1016/j.jde.2021.01.002.

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16

Jensen, Robert, and Andrzej Świech. "Uniqueness and existence of maximal and minimal solutions of fully nonlinear elliptic PDE." Communications on Pure & Applied Analysis 4, no. 1 (2005): 199–207. http://dx.doi.org/10.3934/cpaa.2005.4.187.

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17

Kong, Tao, Weidong Zhao, and Tao Zhou. "Probabilistic High Order Numerical Schemes for Fully Nonlinear Parabolic PDEs." Communications in Computational Physics 18, no. 5 (2015): 1482–503. http://dx.doi.org/10.4208/cicp.240515.280815a.

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AbstractIn this paper, we are concerned with probabilistic high order numerical schemes for Cauchy problems of fully nonlinear parabolic PDEs. For such parabolic PDEs, it is shown by Cheridito, Soner, Touzi and Victoir [4] that the associated exact solutions admit probabilistic interpretations, i.e., the solution of a fully nonlinear parabolic PDE solves a corresponding second order forward backward stochastic differential equation (2FBSDEs). Our numerical schemes rely on solving those 2FBSDEs, by extending our previous results [W. Zhao, Y. Fu and T. Zhou, SIAM J. Sci. Comput., 36 (2014), pp.

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18

Caffarelli, Luis A., and Panagiotis E. Souganidis. "Rates of convergence for the homogenization of fully nonlinear uniformly elliptic pde in random media." Inventiones mathematicae 180, no. 2 (2010): 301–60. http://dx.doi.org/10.1007/s00222-009-0230-6.

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19

Philippin, G. A., and A. Safoui. "Some applications of the maximum principle to a variety of fully nonlinear elliptic PDE?s." Zeitschrift f�r Angewandte Mathematik und Physik (ZAMP) 54, no. 5 (2003): 739–55. http://dx.doi.org/10.1007/s00033-003-3200-7.

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20

Han, Yuecai, and Chunyang Liu. "Asian Option Pricing under an Uncertain Volatility Model." Mathematical Problems in Engineering 2020 (April 21, 2020): 1–10. http://dx.doi.org/10.1155/2020/4758052.

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In this paper, we study the asymptotic behavior of Asian option prices in the worst-case scenario under an uncertain volatility model. We derive a procedure to approximate Asian option prices with a small volatility interval. By imposing additional conditions on the boundary condition and splitting the obtained Black–Scholes–Barenblatt equation into two Black–Scholes-like equations, we obtain an approximation method to solve a fully nonlinear PDE.

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21

Wang, Pei-Yong. "REGULARITY OF FREE BOUNDARIES OF TWO-PHASE PROBLEMS FOR FULLY NONLINEAR ELLIPTIC EQUATIONS OF SECOND ORDER. II. FLAT FREE BOUNDARIES ARE LIPSCHITZ." Communications in Partial Differential Equations 27, no. 7-8 (2002): 1497–514. http://dx.doi.org/10.1081/pde-120005846.

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22

Lindstrom, Michael R., and Andrea L. Bertozzi. "Qualitative features of a nonlinear, nonlocal, agent-based PDE model with applications to homelessness." Mathematical Models and Methods in Applied Sciences 30, no. 10 (2020): 1863–91. http://dx.doi.org/10.1142/s0218202520400114.

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In this paper, we develop a continuum model for the movement of agents on a lattice, taking into account location desirability, local and far-range migration, and localized entry and exit rates. Specifically, our motivation is to qualitatively describe the homeless population in Los Angeles. The model takes the form of a fully nonlinear, nonlocal, non-degenerate parabolic partial differential equation. We derive the model and prove useful properties of smooth solutions, including uniqueness and [Formula: see text]-stability under certain hypotheses. We also illustrate numerical solutions to th

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23

Katzourakis, Nikos. "On linear degenerate elliptic PDE systems with constant coefficients." Advances in Calculus of Variations 9, no. 3 (2016): 283–91. http://dx.doi.org/10.1515/acv-2015-0004.

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AbstractLet ${\mathbf{A}}$ be a symmetric convex quadratic form on ${\mathbb{R}^{Nn}}$ and Ω $\subset$$\mathbb{R}^{n}$ a bounded convex domain. We consider the problem of existence of solutions u: Ω $\subset$$\mathbb{R}^{n}$$\to$$\mathbb{R}^{N}$ to the problem${}\left\{\begin{aligned} \displaystyle\sum_{\beta=1}^{N}\sum_{i,j=1}^{n}% \mathbf{A}_{\alpha i\beta j}D^{2}_{ij}u_{\beta}&\displaystyle=f_{\alpha}&&% \displaystyle\text{in }\Omega,\\ \displaystyle u&\displaystyle=0&&\displaystyle\text{on }\partial\Omega,\end{% aligned}\right.\phantom{\}}$when ${f\in L^{2}(\Omega,\

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24

Katzourakis, Nikos, and Tristan Pryer. "Second-order L∞ variational problems and the ∞-polylaplacian." Advances in Calculus of Variations 13, no. 2 (2020): 115–40. http://dx.doi.org/10.1515/acv-2016-0052.

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AbstractIn this paper we initiate the study of second-order variational problems in {L^{\infty}}, seeking to minimise the {L^{\infty}} norm of a function of the hessian. We also derive and study the respective PDE arising as the analogue of the Euler–Lagrange equation. Given {\mathrm{H}\in C^{1}(\mathbb{R}^{n\times n}_{s})}, for the functional\mathrm{E}_{\infty}(u,\mathcal{O})=\|\mathrm{H}(\mathrm{D}^{2}u)\|_{L^{\infty}% (\mathcal{O})},\quad u\in W^{2,\infty}(\Omega),\mathcal{O}\subseteq\Omega,{}the associated equation is the fully nonlinear third-order PDE\mathrm{A}^{2}_{\infty}u:=(\mathrm{H}

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25

Katzourakis, Nikos. "Weak vs. 𝒟-solutions to linear hyperbolic first-order systems with constant coefficients". Journal of Hyperbolic Differential Equations 15, № 02 (2018): 329–47. http://dx.doi.org/10.1142/s0219891618500121.

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We establish a consistency result by comparing two independent notions of generalized solutions to a large class of linear hyperbolic first-order PDE systems with constant coefficients, showing that they eventually coincide. The first is the usual notion of weak solutions defined via duality. The second is the new notion of [Formula: see text]-solutions which we recently introduced and arose in connection to the vectorial calculus of variations in [Formula: see text] and fully nonlinear elliptic systems. This new approach is a duality-free alternative to distributions and is based on the proba

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26

Grün, G., and P. Weiß. "On the field-induced transport of magnetic nanoparticles in incompressible flow: Modeling and numerics." Mathematical Models and Methods in Applied Sciences 29, no. 12 (2019): 2321–57. http://dx.doi.org/10.1142/s0218202519500477.

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By methods from non-equilibrium thermodynamics, we derive a class of nonlinear pde-models to describe the motion of magnetizable nanoparticles suspended in incompressible carrier fluids under the influence of external magnetic fields. Our system of partial differential equations couples Navier–Stokes and magnetostatic equations to evolution equations for the magnetization field and the particle number density. In the second part of the paper, a fully discrete mixed finite-element scheme is introduced which is rigorously shown to be energy-stable. Finally, we present numerical simulations in th

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27

Zhang, Yanmei, Xia Cui, and Guangwei Yuan. "Nonlinear iteration acceleration solution for equilibrium radiation diffusion equation." ESAIM: Mathematical Modelling and Numerical Analysis 54, no. 5 (2020): 1465–90. http://dx.doi.org/10.1051/m2an/2019095.

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This paper discusses accelerating iterative methods for solving the fully implicit (FI) scheme of equilibrium radiation diffusion problem. Together with the FI Picard factorization (PF) iteration method, three new nonlinear iterative methods, namely, the FI Picard-Newton factorization (PNF), FI Picard-Newton (PN) and derivative free Picard-Newton factorization (DFPNF) iteration methods are studied, in which the resulting linear equations can preserve the parabolic feature of the original PDE. By using the induction reasoning technique to deal with the strong nonlinearity of the problem, rigoro

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28

Jandačka, Martin, and Daniel Ševčovič. "On the risk-adjusted pricing-methodology-based valuation of vanilla options and explanation of the volatility smile." Journal of Applied Mathematics 2005, no. 3 (2005): 235–58. http://dx.doi.org/10.1155/jam.2005.235.

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We analyse a model for pricing derivative securities in the presence of both transaction costs as well as the risk from a volatile portfolio. The model is based on the Black-Scholes parabolic PDE in which transaction costs are described following the Hoggard, Whalley, and Wilmott approach. The risk from a volatile portfolio is described by the variance of the synthesized portfolio. Transaction costs as well as the volatile portfolio risk depend on the time lag between two consecutive transactions. Minimizing their sum yields the optimal length of the hedge interval. In this model, prices of va

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29

Di Francesco, Marco, and Simone Fagioli. "A nonlocal swarm model for predators–prey interactions." Mathematical Models and Methods in Applied Sciences 26, no. 02 (2015): 319–55. http://dx.doi.org/10.1142/s0218202516400042.

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We consider a two-species system of nonlocal interaction PDEs modeling the swarming dynamics of predators and prey, in which all agents interact through attractive/repulsive forces of gradient type. In order to model the predator–prey interaction, we prescribed proportional potentials (with opposite signs) for the cross-interaction part. The model has a particle-based discrete (ODE) version and a continuum PDE version. We investigate the structure of particle stationary solution and their stability in the ODE system in a systematic form, and then consider simple examples. We then prove that th

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30

Long, Kevin, Paul T. Boggs, and Bart G. van Bloemen Waanders. "Sundance: High-Level Software for PDE-Constrained Optimization." Scientific Programming 20, no. 3 (2012): 293–310. http://dx.doi.org/10.1155/2012/380908.

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Sundance is a package in the Trilinos suite designed to provide high-level components for the development of high-performance PDE simulators with built-in capabilities for PDE-constrained optimization. We review the implications of PDE-constrained optimization on simulator design requirements, then survey the architecture of the Sundance problem specification components. These components allow immediate extension of a forward simulator for use in an optimization context. We show examples of the use of these components to develop full-space and reduced-space codes for linear and nonlinear PDE-c

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31

Hamer, Russell D., and Christopher W. Tyler. "Phototransduction: Modeling the primate cone flash response." Visual Neuroscience 12, no. 6 (1995): 1063–82. http://dx.doi.org/10.1017/s0952523800006726.

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AbstractWe have developed a new model of phototransduction that accounts for the dynamics of primate and human cone flash responses in both their linear and saturating range. The model incorporates many of the known elements of the phototransduction cascade in vertebrate photoreceptors. The input stage is a new analytic expression for the activation and inactivation of cGMP-phosphodiesterase (PDE). Although the Lamb and Pugh (1992) model (of a delayed ramp for the rising phase of the PDE* response in amphibian rods) provided a good fit for the first 2 log units of stimulus intensity without pa

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32

Zhao, Xiaodong, Jianzhong Cao, Zuofeng Zhou, and Jijiang Huang. "A Novel PDE-Based Single Image Super-Resolution Reconstruction Method." International Journal of Pattern Recognition and Artificial Intelligence 31, no. 06 (2017): 1754010. http://dx.doi.org/10.1142/s0218001417540106.

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For applications such as remote sensing imaging and medical imaging, high-resolution (HR) images are urgently required. Image Super-Resolution (SR) reconstruction has great application prospects in optical imaging. In this paper, we propose a novel unified Partial Differential Equation (PDE)-based method to single image SR reconstruction. Firstly, two directional diffusion terms calculated by Anisotropic Nonlinear Structure Tensor (ANLST) are constructed, combing information of all channels to prevent singular results, making full use of its directional diffusion feature. Secondly, by introduc

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33

Chen, Lidao, and Yong Liu. "Differential Quadrature Method for Fully Intrinsic Equations of Geometrically Exact Beams." Aerospace 9, no. 10 (2022): 596. http://dx.doi.org/10.3390/aerospace9100596.

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In this paper, a differential quadrature method of high-order precision (DQ−Pade), which is equivalent to the generalized Pade approximation for approximating the end of a time or spatial interval, is used to solve nonlinear fully intrinsic equations of beams. The equations are a set of first-order differential equations with respect to time and space, and the explicit unknowns of the equations involve only forces, moments, velocity and angular velocity, without displacements and rotations. Based on the DQ−Pade method, the spatial and temporal discrete forms of fully intrinsic equations were d

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34

Yang, Haijian, Feng-Nan Hwang, and Xiao-Chuan Cai. "Nonlinear Preconditioning Techniques for Full-Space Lagrange--Newton Solution of PDE-Constrained Optimization Problems." SIAM Journal on Scientific Computing 38, no. 5 (2016): A2756—A2778. http://dx.doi.org/10.1137/15m104075x.

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35

El hajaji, Abdelmajid, Khalid Hilal, Abdelhafid Serghini, and El bekkey Mermri. "Pricing American bond options using a cubic spline collocation method." Boletim da Sociedade Paranaense de Matemática 32, no. 2 (2014): 189. http://dx.doi.org/10.5269/bspm.v32i2.21354.

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In this paper, American options on a discount bond are priced under the Cox-Ingrosll-Ross (CIR) model. The linear complementarity problem of the option value is solved numerically by a penalty method. The problem is transformed into a nonlinear partial differential equation (PDE) by adding a power penalty term. The solution of the penalized problem converges to the one of the original problem. To numerically solve this nonlinear PDE, we use the horizontal method of lines to discretize the temporal variable and the spatial variable by means of trapezoidal method and a cubic spline collocation m

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36

Garde, Smita, Michael G. Regalado, Vicki L. Schechtman, and Michael C. K. Khoo. "Nonlinear dynamics of heart rate variability in cocaine-exposed neonates during sleep." American Journal of Physiology-Heart and Circulatory Physiology 280, no. 6 (2001): H2920—H2928. http://dx.doi.org/10.1152/ajpheart.2001.280.6.h2920.

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The aim of this study was to determine the effects of prenatal cocaine exposure (PCE) on the dynamics of heart rate variability in full-term neonates during sleep. R-R interval (RRI) time series from 9 infants with PCE and 12 controls during periods of stable quiet sleep and active sleep were analyzed using autoregressive modeling and nonlinear dynamics. There were no differences between the two groups in spectral power distribution, approximate entropy, correlation dimension, and nonlinear predictability. However, application of surrogate data analysis to these measures revealed a significant

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37

Hall, E., S. Kessler, and S. Hanagud. "Use of Fractal Dimension in the Characterization of Chaotic Structural Dynamic Sytems." Applied Mechanics Reviews 44, no. 11S (1991): S107—S113. http://dx.doi.org/10.1115/1.3121342.

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The purpose of this paper is to investigate the use of fractal dimensions in the characterization of chaotic systems in structural dynamics. The investigation focuses on the example of a simply-supported, Euler-Bernoulli beam which when subjected to a transverse forcing function of a particular amplitude responds chaotically. Three different nonlinear models of the system are studied: a complex partial differential equation (PDE) model, a simplified PDE model, and a Galerkin approximation to the simpler PDE model. The responses of each model are examined through zero velocity Poincare´ section

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38

Hwang, Feng-Nan. "Three-dimensional trajectory optimization for multi-stage launch vehicle mission using a full-space quasi-Lagrange–Newton method." ANZIAM Journal 60 (August 30, 2019): C172—C186. http://dx.doi.org/10.21914/anziamj.v60i0.14067.

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Many aerospace industrial applications require robust and efficient numerical solutions of large sparse nonlinear constrained parameter optimization problems arising from optimal trajectory problems. A three-dimensional multistage launcher problem is taken as a numerical example for studying the performance and applicability of the full-space Lagrange–Newton–Krylov method. The typical optimal trajectory, control history and other important physical qualities are presented, and the efficiency of the algorithm is also investigated.  References J. T. Betts. Practical methods for optim

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39

Said, Hamid. "An analytical mechanics approach to the first law of thermodynamics and construction of a variational hierarchy." Theoretical and Applied Mechanics, no. 00 (2020): 11. http://dx.doi.org/10.2298/tam200315011s.

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A simple procedure is presented for the study of the conservation of energy equation with dissipation in continuum mechanics in 1D. This procedure is used to transform this nonlinear evolution-diffusion equation into a hyperbolic PDE; specifically, a second-order quasi-linear wave equation. An immediate implication of this procedure is the formation of a least action principle for the balance of energy with dissipation. The corresponding action functional enables us to establish a complete analytic mechanics for thermomechanical systems: a Lagrangian-Hamiltonian theory, integrals of motion, br

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40

Sieber, J., M. Radžiūnas, and K. R. Schneider. "DYNAMICS OF MULTISECTION SEMICONDUCTOR LASERS." Mathematical Modelling and Analysis 9, no. 1 (2005): 51–66. http://dx.doi.org/10.3846/13926292.2004.9637241.

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We investigate the longitudinal dynamics of multisection semiconductor lasers based on a model, where a hyperbolic system of partial differential equations is nonlinearly coupled with a system of ordinary differential equations. We present analytic results for that system: global existence and uniqueness of the initial‐boundary value problem, and existence of attracting invariant manifolds of low dimension. The flow on these manifolds is approximately described by the so‐called mode approximations which are systems of ordinary differential equations. Finally, we present a detailed numerical bi

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41

COMAN, Calin-Dumitru. "The Influence of Temperature on the Strength of Hybrid Metal-Composite Multi-Bolts Joints." INCAS BULLETIN 12, no. 3 (2020): 49–64. http://dx.doi.org/10.13111/2066-8201.2020.12.3.4.

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This paper presents the temperature influence on the strength of the hybrid metal-composite multi-bolted joints. A detailed 3D finite element model, incorporating all possible nonlinearities as large deformations, in plane nonlinear shear deformations, elastic properties degradation of the composite material and friction-based full contact, is developed to anticipate the temperature changing effects on the progressive damage analysis (PDA) at lamina level and failure modes of metal-composite multi-bolted joints. The PDA material model accounts for lamina nonlinear shear deformation, Hashin-typ

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42

Djouadi, Seddik M., R. Chris Camphouse, and James H. Myatt. "Empirical Reduced-Order Modeling for Boundary Feedback Flow Control." Journal of Control Science and Engineering 2008 (2008): 1–11. http://dx.doi.org/10.1155/2008/154956.

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This paper deals with the practical and theoretical implications of model reduction for aerodynamic flow-based control problems. Various aspects of model reduction are discussed that apply to partial differential equation- (PDE-) based models in general. Specifically, the proper orthogonal decomposition (POD) of a high dimension system as well as frequency domain identification methods are discussed for initial model construction. Projections on the POD basis give a nonlinear Galerkin model. Then, a model reduction method based on empirical balanced truncation is developed and applied to the G

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43

Dumbser, Michael, and Eleuterio F. Toro. "On Universal Osher-Type Schemes for General Nonlinear Hyperbolic Conservation Laws." Communications in Computational Physics 10, no. 3 (2011): 635–71. http://dx.doi.org/10.4208/cicp.170610.021210a.

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This paper is concerned with a new version of the Osher-Solomon Riemann solver and is based on a numerical integration of the path-dependent dissipation matrix. The resulting scheme is much simpler than the original one and is applicable to general hyperbolic conservation laws, while retaining the attractive features of the original solver: the method is entropy-satisfying, differentiable and complete in the sense that it attributes a different numerical viscosity to each characteristic field, in particular to the intermediate ones, since the full eigenstructure of the underlying hyperbolic sy

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44

Kraus, Johannes, Svetoslav Nakov, and Sergey I. Repin. "Reliable Numerical Solution of a Class of Nonlinear Elliptic Problems Generated by the Poisson–Boltzmann Equation." Computational Methods in Applied Mathematics 20, no. 2 (2020): 293–319. http://dx.doi.org/10.1515/cmam-2018-0252.

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AbstractWe consider a class of nonlinear elliptic problems associated with models in biophysics, which are described by the Poisson–Boltzmann equation (PBE). We prove mathematical correctness of the problem, study a suitable class of approximations, and deduce guaranteed and fully computable bounds of approximation errors. The latter goal is achieved by means of the approach suggested in [19] for convex variational problems. Moreover, we establish the error identity, which defines the error measure natural for the considered class of problems and show that it yields computable majorants and mi

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COMAN, Calin-Dumitru. "Influence of Geometry on Failure Modes of Hybrid Metal-Composite Protruding Bolted Joints." INCAS BULLETIN 13, no. 3 (2021): 29–44. http://dx.doi.org/10.13111/2066-8201.2021.13.3.3.

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This article presents the influence of joint geometry on the damage mode in the CFRP (Carbon Fiber Reinforced Polymer) composite plate of the single-lap, protruding, hybrid metal-composite joints. A detailed 3D finite element model incorporating geometric, material and friction-based contact full nonlinearities is developed to numerically investigate the geometry effects on the progressive damage analysis (PDA) of the orthotropic material model. The PDA material model integrates the nonlinear shear response, Hashin-tape failure criteria and strain-based continuum degradation rules being develo

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CHRISTOV, C. I., and M. G. VELARDE. "INELASTIC INTERACTION OF BOUSSINESQ SOLITONS." International Journal of Bifurcation and Chaos 04, no. 05 (1994): 1095–112. http://dx.doi.org/10.1142/s0218127494000800.

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Two improved versions of Boussinesq equation (Boussinesq paradigm) have been considered which are well-posed (correct in the sense of Hadamard) as an initial value problem: the Proper Boussinesq Equation (PBE) and the Regularized Long Wave Equation (RLWE). Fully implicit difference schemes have been developed strictly representing, on difference level, the conservation or balance laws for the mass, pseudoenergy or pseudomomentum of the wave system. Thresholds of possible nonlinear blow-up are identified for both PBE and RLWE. The head-on collisions of solitary waves of the sech type (Boussines

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Jovanović, Radiša, Vladimir Zarić, Zoran Bučevac, and Uglješa Bugarić. "Discrete-Time System Conditional Optimization Based on Takagi–Sugeno Fuzzy Model Using the Full Transfer Function." Applied Sciences 12, no. 15 (2022): 7705. http://dx.doi.org/10.3390/app12157705.

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The study proposes a novel method for synthesis of a discrete-time parallel distributed compensation (PDC) controller for the nonlinear discrete-time Takagi–Sugeno (TS) fuzzy plant model. For each of the fuzzy plant model linear subsystems, a local linear first order proportional-sum (PS) controller is designed. The algebraic technique is used in two-dimensional parameter space, utilizing the characteristic polynomial of the row nondegenerate full transfer function matrix. Each system’s relative stability is accomplished in relation to the selected damping coefficient. The supplementary criter

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GUTIERREZ, GAIL, and WHADY FLOREZ. "COMPARISON BETWEEN GLOBAL, CLASSICAL DOMAIN DECOMPOSITION AND LOCAL, SINGLE AND DOUBLE COLLOCATION METHODS BASED ON RBF INTERPOLATION FOR SOLVING CONVECTION-DIFFUSION EQUATION." International Journal of Modern Physics C 19, no. 11 (2008): 1737–51. http://dx.doi.org/10.1142/s0129183108013102.

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This work presents a performance comparison of several meshless RBF formulations for convection-diffusion equation with moderate-to-high Peclet number regimes. For the solution of convection-diffusion problems, several comparisons between global (full-domain) meshless RBF methods and mesh-based methods have been presented in the literature. However, in depth studies between new local RBF collocation methods and full-domain symmetric RBF collocation methods are not reported yet. The RBF formulations included: global symmetric method, symmetric double boundary collocation method, additive Schwar

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COMAN, Calin-Dumitru. "Influence of Preload on Failure Modes of Hybrid Metal-Composite Protruding Bolted Joints." INCAS BULLETIN 13, no. 1 (2021): 29–41. http://dx.doi.org/10.13111/2066-8201.2021.13.1.4.

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This paper presents the effects of torque preload on the damage initiation and growth in the CFRP (Carbon Fiber Reinforced Polymer) composite laminated adherent of the single-lap, single-bolt, hybrid metal-composite joints. A detailed 3D finite element model incorporating geometric, material and friction-based contact full nonlinearities is developed to numerically investigate the preload effects on the progressive damage analysis (PDA) of the orthotropic material model. The PDA material model integrates the nonlinear shear response, Hashin-tape failure criteria and strain-based continuum elas

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Coman, Calin Dumitru, and Dan Mihai Constantinescu. "Preload Effects on Failure Mechanisms of Hybrid Metal-Composite Bolted Joints." Materials Science Forum 957 (June 2019): 293–302. http://dx.doi.org/10.4028/www.scientific.net/msf.957.293.

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This paper presents the effects of torque preload on the damage initiation and growth in the CFRP (Carbon Fiber Reinforced Polymer) composite laminated adherent of the single-lap, single-bolt, hybrid metal-composite joints. A detailed 3D finite element model incorporating geometric, material and friction-based contact full nonlinearities is developed to numerically investigate the preload effects on the progressive damage analysis (PDA) of the orthotropic material model. The PDA material model integrates the nonlinear shear response, Hashin-tape failure criteria and strain-based continuum elas

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