Bibliographies thématiques / Nonlinear PDE`s

Littérature scientifique sur le sujet « Nonlinear PDE`s »

Auteur : Grafiati

Publié le 18 mai 2024

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Articles de revues sur le sujet "Nonlinear PDE`s"

Khodja, Brahim. « A nonexistence result for a nonlinear PDE with Robin condition ». International Journal of Mathematics and Mathematical Sciences 2006 (2006) : 1–12. http://dx.doi.org/10.1155/ijmms/2006/62601.

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Under the assumptionλ>0andfverifyingf(x,y,0)=0inD,2F(x,y,u)−uf(x,y,u)≥0,u≠0, and ifΩ=R×D, we show the convexity of functionE(t)=∬D|u(t,x,y)|2dxdy, whereu:Ω→ℝis a solution of problemλ(∂2u/∂t2)−(∂/∂x)(p(x,y)(∂u/∂x))−(∂/∂y)(q(x,y)(∂u/∂y))+f(x,y,u)=0 in Ω,u+ε(∂u/∂n)=0 on ∂Ω, considered inH2(Ω)∩L∞(Ω),p,q:D¯→ℝare two nonnull functions onD,εis a positive real number, andD=]a1,b1[×]a2,b2[,(F(x,y,s)=∫0sf(x,y,t)dt).

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Geldhauser, Carina, et Enrico Valdinoci. « Optimizing the Fractional Power in a Model with Stochastic PDE Constraints ». Advanced Nonlinear Studies 18, n^o 4 (1 novembre 2018) : 649–69. http://dx.doi.org/10.1515/ans-2018-2031.

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AbstractWe study an optimization problem with SPDE constraints, which has the peculiarity that the control parameter s is the s-th power of the diffusion operator in the state equation. Well-posedness of the state equation and differentiability properties with respect to the fractional parameter s are established. We show that under certain conditions on the noise, optimality conditions for the control problem can be established.

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Ji, Binxin, Xiangxing Tao et Yanting Ji. « Barrier Option Pricing in the Sub-Mixed Fractional Brownian Motion with Jump Environment ». Fractal and Fractional 6, n^o 5 (29 avril 2022) : 244. http://dx.doi.org/10.3390/fractalfract6050244.

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This paper investigates the pricing formula for barrier options where the underlying asset is driven by the sub-mixed fractional Brownian motion with jump. By applying the corresponding Ito^’s formula, the B-S type PDE is derived by a self-financing strategy. Furthermore, the explicit pricing formula for barrier options is obtained through converting the PDE to the Cauchy problem. Numerical experiments are conducted to test the impact of the barrier price, the Hurst index, the jump intensity and the volatility on the value of barrier option respectively.

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KNESSL, CHARLES. « Asymptotic analysis of the American call option with dividends ». European Journal of Applied Mathematics 13, n^o 6 (décembre 2002) : 587–616. http://dx.doi.org/10.1017/s0956792502004898.

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We consider an American call option and let C(S, T0) be the price of an option corresponding to asset price S at some time T0 prior to the expiration time TF . We analyze C(S, T0) in various asymptotic limits. These include situations where the interest and dividend rates are large or small, compared to the volatility of the asset. We also analyze the optimal exercise boundary for the option. We use perturbation methods to analyze either the PDE that C(S, T0) satisfies, or a nonlinear integral equation that is satisfied by the optimal exercise boundary.

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Philippin, G. A., et 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, n^o 5 (1 septembre 2003) : 739–55. http://dx.doi.org/10.1007/s00033-003-3200-7.

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Bonazebi-Yindoula, Joseph. « Laplace-SBA Method for Solving Nonlinear Coupled Burger's Equations ». European Journal of Pure and Applied Mathematics 14, n^o 3 (5 août 2021) : 842–62. http://dx.doi.org/10.29020/nybg.ejpam.v14i3.3932.

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Burgerâ€™s equations, an extension of fluid dynamics equations, are typically solved by several numerical methods. In this article, the laplace-SomÃ© Blaise Abbo method is used to solve nonlinear Burger equations. This method is based on the combination of the laplace transform and the SBA method. After reminders of the laplace transform, the basic principles of the SBA method are described. The process of calculating the Laplace-SBA algorithm for determining the exact solution of a linear or nonlinear partial derivative equation is shown. Thus, three examplesof PDE are solved by this method, which all lead to exact solutions. Our results suggest that this method can be extended to other more complex PDEs.

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Cavalcanti, Marcelo M., Valéria N. Domingos Cavalcanti, Irena Lasiecka et Claudete M. Webler. « Intrinsic decay rates for the energy of a nonlinear viscoelastic equation modeling the vibrations of thin rods with variable density ». Advances in Nonlinear Analysis 6, n^o 2 (1 mai 2017) : 121–45. http://dx.doi.org/10.1515/anona-2016-0027.

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AbstractWe consider the long-time behavior of a nonlinear PDE with a memory term which can be recast in the abstract form$\frac{d}{dt}\rho(u_{t})+Au_{tt}+\gamma A^{\theta}u_{t}+Au-\int_{0}^{t}g(s)Au(t% -s)=0,$where A is a self-adjoint, positive definite operator acting on a Hilbert space H, ${\rho(s)}$ is a continuous, monotone increasing function, and the relaxation kernel ${g(s)}$ is a continuous, decreasing function in ${L_{1}(\mathbb{R}_{+})}$ with ${g(0)>0}$. Of particular interest is the case when ${A=-\Delta}$ with appropriate boundary conditions and ${\rho(s)=|s|^{\rho}s}$. This model arises in the context of solid mechanics accounting for variable density of the material. While finite energy solutions of the underlying PDE solutions exhibit exponential decay rates when strong damping is active (${\gamma>0,\theta=1}$), this uniform decay is no longer valid (by spectral analysis arguments) for dynamics subjected to frictional damping only, say, ${\theta=0}$ and ${g=0}$. In the absence of mechanical damping (${\gamma=0}$), the linearized version of the model reduces to a Volterra equation generated by bounded generators and, hence, it is exponentially stable for exponentially decaying kernels. The aim of the paper is to study intrinsic decays for the energy of the nonlinear model accounting for large classes of relaxation kernels described by the inequality ${g^{\prime}+H(g)\leq 0}$ with H convex and subject to the assumptions specified in (1.13) (a general framework introduced first in [1] in the context of linear second-order evolution equations with memory). In the context of frictional damping, such a framework was introduced earlier in [15], where it was shown that the decay rates of second-order evolution equations with frictional damping can be described by solutions of an ODE driven by a suitable convex function H which captures the behavior at the origin of the dissipation. The present paper extends this analysis to nonlinear equations with viscoelasticity. It is shown that the decay rates of the energy are intrinsically described by the solution of the dissipative ODE${S_{t}+c_{1}H(c_{2}S)=0}$with given intrinsic constants ${c_{1},c_{2}>0}$. The results obtained are sharp and they improve (by introducing a novel methodology) previous results in the literature (see [20, 19, 21, 6]) with respect to (i) the criticality of the nonlinear exponent ρ and (ii) the generality of the relaxation kernel.

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Bridges, Thomas J. « Canonical multi-symplectic structure on the total exterior algebra bundle ». Proceedings of the Royal Society A : Mathematical, Physical and Engineering Sciences 462, n^o 2069 (8 février 2006) : 1531–51. http://dx.doi.org/10.1098/rspa.2005.1629.

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The aim of this paper is to construct multi-symplectic structures starting with the geometry of an oriented Riemannian manifold, independent of a Lagrangian or a particular partial differential equation (PDE). The principal observation is that on an n -dimensional orientable manifold M there is a canonical quadratic form Θ associated with the total exterior algebra bundle on M . On the fibre, which has dimension 2 n , the form Θ can be locally decomposed into n classical symplectic structures. When concatenated, these n -symplectic structures define a partial differential operator, J ∂ , which turns out to be a Dirac operator with multi-symplectic structure. The operator J ∂ generalizes the product operator J (d/d t ) in classical symplectic geometry, and M is a generalization of the base manifold (i.e. time) in classical Hamiltonian dynamics. The structure generated by Θ provides a natural setting for analysing a class of covariant nonlinear gradient elliptic operators. The operator J ∂ is elliptic, and the generalization of Hamiltonian systems, J ∂ Z =∇ S ( Z ), for a section Z of the total exterior algebra bundle, is also an elliptic PDE. The inverse problem—find S ( Z ) for a given elliptic PDE—is shown to be related to a variant of the Legendre transform on k -forms. The theory is developed for flat base manifolds, but the constructions are coordinate free and generalize to Riemannian manifolds with non-trivial curvature. Some applications and implications of the theory are also discussed.

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Wei, Hongbo, Xuerong Cui, Yucheng Zhang et Jingyao Zhang. « $ H_\infty $ deployment of nonlinear multi-agent systems with Markov switching topologies over a finite-time interval based on T–S fuzzy PDE control ». AIMS Mathematics 9, n^o 2 (2024) : 4076–97. http://dx.doi.org/10.3934/math.2024199.

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<abstract><p>The deployment of multi-agent systems (MASs) is widely used in the fields of unmanned agricultural machineries, unmanned aerial vehicles, intelligent transportation, etc. To make up for the defect that the existing PDE-based results are overly idealistic in terms of system models and control strategies, we study the PDE-based deployment of clustered nonlinear first-order and second-order MASs over a finite-time interval (FTI). By designing special communication protocols, the collective dynamics of numerous agents are modeled by simple fist-order and second-order PDEs. Two practical factors, external disturbance and Markov switching topology, are considered in this paper to better match actual situations. Besides, T–S fuzzy technology is used to approximate the unknown nonlinearity of MASs. Then, by using boundary control scheme with collocated measurements, two theorems are obtained to ensure the finite-time $ H_\infty $ deployment of first-order and second-order agents, respectively. Finally, numerical examples are provided to illustrate the effectiveness of the proposed approaches.</p></abstract>

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Daoues, Adel, Amani Hammami et Kamel Saoudi. « Multiple positive solutions for a nonlocal PDE with critical Sobolev-Hardy and singular nonlinearities via perturbation method ». Fractional Calculus and Applied Analysis 23, n^o 3 (25 juin 2020) : 837–60. http://dx.doi.org/10.1515/fca-2020-0042.

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AbstractIn this paper we investigate the following nonlocal problem with singular term and critical Hardy-Sobolev exponent$$\begin{array}{} ({\rm P}) \left\{ \begin{array}{ll} (-\Delta)^s u = \displaystyle{\frac{\lambda}{u^\gamma}+\frac{|u|^{2_\alpha^*-2}u}{|x|^\alpha}} \ \ \text{ in } \ \ \Omega, \\ u >0 \ \ \text{ in } \ \ \Omega, \quad u = 0 \ \ \text{ in } \ \ \mathbb{R}^{N}\setminus \Omega, \end{array} \right. \end{array}$$where Ω ⊂ ℝN is an open bounded domain with Lipschitz boundary, 0 < s < 1, λ > 0 is a parameter, 0 < α < 2s < N, 0 < γ < 1 < 2 < $\begin{array}{} \displaystyle 2_s^* \end{array}$, where $\begin{array}{} \displaystyle 2_s^* = \frac{2N}{N-2s} ~\text{and}~ 2_\alpha^* = \frac{2(N-\alpha)}{N-2s} \end{array}$ are the fractional critical Sobolev and Hardy Sobolev exponents respectively. The fractional Laplacian (–Δ)s with s ∈ (0, 1) is the nonlinear nonlocal operator defined on smooth functions by$$\begin{array}{} \displaystyle (-\Delta)^s u(x)=-\frac{1}{2} \displaystyle\int_{\mathbb{R}^N} \frac{u(x+y)+u(x-y)-2u(x)}{|y|^{N+2s}}{\rm d }y, \;\; \text{ for all }\, x \in \mathbb{R}^N. \end{array}$$By combining variational and approximation methods, we provide the existence of two positive solutions to the problem (P).

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Plus de sources

Chapitres de livres sur le sujet "Nonlinear PDE`s"

Van Barel, Marc, et Adhemar Bultheel. « Minimal Pade-Sense Matrix Approximations Around s = 0 and s = ∞ ». Dans Nonlinear Numerical Methods and Rational Approximation, 143–54. Dordrecht : Springer Netherlands, 1988. http://dx.doi.org/10.1007/978-94-009-2901-2_8.

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Actes de conférences sur le sujet "Nonlinear PDE`s"

Daisuke Akasaka et Kang-Zhi Liu. « Nonlinear feedback control of a class of on-off control systems : An approach based on analytical solution of PDE’s ». Dans 2007 46th IEEE Conference on Decision and Control. IEEE, 2007. http://dx.doi.org/10.1109/cdc.2007.4434227.

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Psaltis, Demetri, Hsin-Yu Li, Yong Qiao et Kevin Curtis. « Optical Image Recognition System Implemented with a 3-D Memory Disk ». Dans Nonlinear Optics. Washington, D.C. : Optica Publishing Group, 1992. http://dx.doi.org/10.1364/nlo.1992.pd5.

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Holographic storage of data in 3-D media can provide high density of information storage and parallel access to the stored information. Such memories were investigated extensively in the early 60’s [1,2,3,4,5] and even though these early efforts produced remarkable results they never found practical application largely because of material limitations such as low sensitivity, fanning, and hologram decay. Interest in holographic 3-D memories has been revitalized in recent years for a variety of reasons, the most significant probably being the emergence of applications, such as neural networks, machine vision, and databases, that can make use of the capabilities of holographic 3-D memories.

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Ellis, A. D., et D. M. Spirit. « The use of GaInAsP amplifiers for 40 Gbit/s signal processing. » Dans Nonlinear Guided-Wave Phenomena. Washington, D.C. : Optica Publishing Group, 1993. http://dx.doi.org/10.1364/nlgwp.1993.pd.2.

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Optical time domain multiplexed (OTDM) systems are expected to play an important role in increasing the aggregate fibre capacity in telecommunications networks beyond the levels attainable with electronic systems. Within these systems, one of the key elements is a flexible optical demultiplexer, and recently attention has been focused on the use of the Kerr effect in silica based fibres to produce optically controlled switching elements1,2. However, whilst offering attractive functionality, the relatively low nonlinear coefficientin silica fibres leads to excessively long devices and consequent latency, timing and stability issues. It is also necessary to carefully select the fibre properties and signal wavelengths for these switches to achieve a desired function. Thus a compact sub millimetre device, offering similar overall levels of nonlinearity offers clear advantages.

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Cheron, Jerome, Michel Campovecchio, Denis Barataud, Tibault Reveyrand, Sebastien Mons, Michel Stanislawiak, Philippe Eudeline et Didier Floriot. « Design of a 55 W packaged GaN HEMT with 60% PAE by internal matching in S-band ». Dans 2012 Workshop on Integrated Nonlinear Microwave and Millimetre-Wave Circuits (INMMIC). IEEE, 2012. http://dx.doi.org/10.1109/inmmic.2012.6331923.

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Arena, Andrea, Giovanni Formica, Walter Lacarbonara et Harry Dankowicz. « Nonlinear Finite Element-Based Path Following of Periodic Solutions ». Dans ASME 2011 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2011. http://dx.doi.org/10.1115/detc2011-48673.

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A computational framework is proposed to path follow the periodic solutions of nonlinear spatially continuous systems and more general coupled multiphysics problems represented by systems of partial differential equations with time-dependent excitations. The set of PDEs is cast in first order differential form (in time) u˙ = f(u,s,t;c) where u(s,t) is the vector collecting all state variables including the velocities/time rates, s is a space coordinate (here, one-dimensional systems are considered without lack of generality for the space dependence) and t denotes time. The vector field f depends, in general, not only on the classical state variables (such as positions and velocities) but also on the space gradients of the leading unknowns. The space gradients are introduced as part of the state variables. This is justified by the mathematical and computational requirements on the continuity in space up to the proper differential order of the space gradients associated with the unknown position vector field. The path following procedure employs, for the computation of the periodic solutions, only the evaluation of the vector field f. This part of the path following procedure within the proposed combined scheme was formerly implemented by Dankowicz and coworkers in a MATLAB software package called COCO. The here proposed procedure seeks to discretize the space dependence of the variables using finite elements based on Lagrangian polynomials which leads to a discrete form of the vector field f. A concurrent bifurcation analysis is carried out by calculating the eigenvalues of the monodromy matrix. A hinged-hinged nonlinear beam subject to a primary-resonance harmonic transverse load or to a parametric-resonance horizontal end displacement is considered as a case study. Some primary-resonance frequency-response curves are calculated along with their stability to assess the convergence of the discretization scheme. The frequency-response curves are shown to be in close agreement with those calculated by direct integration of the PDEs through the FE software called COMSOL Multiphysics. Besides primary-resonance direct forcing conditions, also parametric forcing causing the principal parametric resonance of the lowest two bending modes is considered through construction of the associated transition curves. The proposed approach integrates algorithms from the finite element and bifurcation domains thus enabling an accurate and effective unfolding of the bifurcation and post-bifurcation scenarios of nonautonomous PDEs with the underlying structures.

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Yuan, Yue, et Xiaojin Huang. « A Fuzzy Control Approach for the Coordinated-Level Control of the Modular-HTGR-Based Nuclear Steam Supplying System ». Dans 2016 24th International Conference on Nuclear Engineering. American Society of Mechanical Engineers, 2016. http://dx.doi.org/10.1115/icone24-60417.

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As one of the most popular Generation IV nuclear energy system, High Temperature Gas Cooled Reactor (HTGR) has outstanding inherent safety features. However, the nonlinearity and complexity of the modular-HTGR-based nuclear steam supplying system (NSSS) has put higher requirements to its control system. Based on the basic ideas and theories of fuzzy system, fuzzy control method provides a powerful tool to the control of nonlinear systems. This paper built the T-S fuzzy model of the modular-HTGR-based nuclear steam supplying system (NSSS), and designed the steam temperature T-S fuzzy controller using the parallel distributed compensation (PDC) method. Simulation shows that the designed T-S fuzzy controller has a better effect than the traditional PID control method.

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Luan, Xiuchun, Jie Zhou et Yu Zhai. « Takagi-Sugeno Fuzzy Load-Following Control of Nuclear Reactors Based on Reactor Point Kinetics Equations ». Dans 2014 22nd International Conference on Nuclear Engineering. American Society of Mechanical Engineers, 2014. http://dx.doi.org/10.1115/icone22-30562.

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A state differential feedback control system based Takagi-Sugeno (T-S) fuzzy model is designed for load-following operation of nonlinear nuclear reactor whose operating points vary within a wide range. Linear models are first derived from the original nonlinear model on several operating points. Next the fuzzy controller is designed via using the parallel distributed compensation (PDC) scheme with the relative neutron density at the equilibrium point as the premise variable. Last the stability analysis is given by means of linear matrix inequality (LMI) approach, thus the control system is guaranteed to be stable within a large range. The simulation results demonstrate that the control system works well over a wide region of operation.

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Romero, Leonel, et W. Kendall Melville. « Observations and Modeling of Linear and Nonlinear Spatio-Temporal Wave Statistics ». Dans ASME 2010 29th International Conference on Ocean, Offshore and Arctic Engineering. ASMEDC, 2010. http://dx.doi.org/10.1115/omae2010-21101.

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We present an analysis of airborne wave observations collected in the Gulf of Tehuantepec. The data includes LIDAR measurements of the surface displacement as a function of two horizontal dimensions and time in fetch-limited conditions, with fetches between 50 and 300 km and winds between 10 and 20 m/s. The spatio-temporal data have an advantage over the commonly used single point time-series measurements allowing direct estimates of the wavelength and wave slope, including spatial information such as the lengths of crests exceeding threshold wave heights and slopes. The statistics of these wave parameters are particularly important for risk assessment of off-shore structures and in other ocean engineering applications. We present an analysis of several statistical wind-wave parameters, including the joint probability distribution function (pdf) of wave amplitudes and wavelengths, the pdf of wave heights, wavenumber vectors, and wave slopes, including the statistics of crests lengths exceeding threshold wave heights or slopes. The empirical findings from the LIDAR data are related to the analytical work by Longuet-Higgins (1957) [1] for a linear spectrum, including the average length of contours surrounding large wave heights. The effect of second-order nonlinearities on the distribution of crest lengths is investigated with numerical stochastic simulations from computed directional wavenumber spectra. The results show that second-order nonlinearities can increase the crest length density of large waves by about a factor of two or more. The results are discussed in the context of predicting wave statistics for ocean engineering applications.

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Johnson, Mark D., et Mohammad A. Ayoubi. « Shared Fuzzy Control of Multiple Quadrotor UAVs With Time-Dependent Delay and Bounded Control-Input Constraint ». Dans ASME 2015 Dynamic Systems and Control Conference. American Society of Mechanical Engineers, 2015. http://dx.doi.org/10.1115/dscc2015-9907.

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We propose a shared fuzzy controller for position and attitude control of multiple quadrotor unmanned aerial vehicles (UAVs). Using the nonlinear governing equations of motion and kinematics of a quadrotor, we develop a Takagi-Sugeno (T-S) fuzzy model for a quadrotor. Then, we consider time-varying delays due to wireless connectioninto the T-S fuzzy model. We use the sufficient stability condition based on the Lyapunov-Krasovskii stability theorem and the parallel distributed compensation (PDC) technique to determine the fuzzy control law. For practical purposes, we include actuator amplitude constraint into the design process. The problem of designing a shared fuzzy controller is cast in the form of linear matrix inequalities (LMIs). A feasible solution region is found in terms of maximum magnitude and rate of time-varying delay. In the end, the stability, performance, and robustness of the proposed shared fuzzy controller are examined via numerical simulation.

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Yu, Haiyan, Xin Zhang et Hongxia Li. « Robust multi-objective and nonlinear control of high-rise elevator vertical motion system based on T-S fuzzy model using PDC and LMIs ». Dans 2009 IEEE International Conference on Automation and Logistics (ICAL). IEEE, 2009. http://dx.doi.org/10.1109/ical.2009.5262743.

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Rapports d'organisations sur le sujet "Nonlinear PDE`s"

Event-Triggered Adaptive Robust Control for Lateral Stability of Steer-by-Wire Vehicles with Abrupt Nonlinear Faults. SAE International, juillet 2022. http://dx.doi.org/10.4271/2022-01-5056.

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Because autonomous vehicles (AVs) equipped with active front steering have the features of time varying, uncertainties, high rate of fault, and high burden on the in-vehicle networks, this article studies the adaptive robust control problem for improving lateral stability in steer-by-wire (SBW) vehicles in the presence of abrupt nonlinear faults. First, an upper-level robust H∞ controller is designed to obtain the desired front-wheel steering angle for driving both the yaw rate and the sideslip angle to reach their correct values. Takagi-Sugeno (T-S) fuzzy modeling method, which has shown the extraordinary ability in coping with the issue of nonlinear, is applied to deal with the challenge of the changing longitudinal velocity. The output of the upper controller can be calculated by a parallel distributed compensation (PDC) scheme. Then an event-triggered adaptive fault-tolerant lower controller (ET-AFTC) is proposed to drive the whole SBW system driving the desired steering angle offered by the upper controller with fewer communication resources and strong robustness. By employing a backstepping technique, the tracking performance is improved. The dynamic surface control (DSC) approach is used to avoid the problem of repeated differentiations, and Nussbaum function is adopted to overcome the difficulty of unknown nonlinear control gain. Both the stability of the upper and lower controllers can be guaranteed by Lyapunov functions. Finally, the simulations of Matlab/Simulink are given to show that the proposed control strategy is effectively able to deal with the abrupt nonlinear fault via less communication resources and perform better in ensuring the yaw stability of the vehicle.

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