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Journal articles on the topic 'Weak maximum principle'

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Author: Grafiati

Published: 9 March 2023

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1

Hamada, Y., H. Kawai, and K. Kawana. "Weak scale from the maximum entropy principle." Progress of Theoretical and Experimental Physics 2015, no. 3 (March 19, 2015): 33B06–0. http://dx.doi.org/10.1093/ptep/ptv011.

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2

Hill, C. Denson, and Mauro Nacinovich. "Weak pseudoconcavity and the maximum modulus principle." Annali di Matematica Pura ed Applicata 182, no. 1 (April 2003): 103–12. http://dx.doi.org/10.1007/s10231-002-0059-8.

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3

Meyer, J. C., and D. J. Needham. "Extended weak maximum principles for parabolic partial differential inequalities on unbounded domains." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 470, no. 2167 (July 8, 2014): 20140079. http://dx.doi.org/10.1098/rspa.2014.0079.

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In this paper, we establish extended maximum principles for solutions to linear parabolic partial differential inequalities on unbounded domains, where the solutions satisfy a variety of growth/decay conditions on the unbounded domain. We establish a conditional maximum principle, which states that a solution u to a linear parabolic partial differential inequality satisfies a maximum principle whenever a suitable weight function can be exhibited. Our extended maximum principles are then established by exhibiting suitable weight functions and applying the conditional maximum principle. In addition, we include several specific examples, to highlight the importance of certain generic conditions, which are required in the statements of maximum principles of this type. Furthermore, we demonstrate how to obtain associated comparison theorems from our extended maximum principles.

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4

Šolín, Pavel, and Tomáš Vejchodský. "A weak discrete maximum principle for hp-FEM." Journal of Computational and Applied Mathematics 209, no. 1 (December 2007): 54–65. http://dx.doi.org/10.1016/j.cam.2006.10.028.

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5

Amendola, M. E., L. Rossi, and A. Vitolo. "Harnack Inequalities and ABP Estimates for Nonlinear Second-Order Elliptic Equations in Unbounded Domains." Abstract and Applied Analysis 2008 (2008): 1–19. http://dx.doi.org/10.1155/2008/178534.

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We are concerned with fully nonlinear uniformly elliptic operators with a superlinear gradient term. We look for local estimates, such as weak Harnack inequality and local maximum principle, and their extension up to the boundary. As applications, we deduce ABP-type estimates and weak maximum principles in general unbounded domains, a strong maximum principle, and a Liouville-type theorem.

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6

Stehlík, Petr, and Jonáš Volek. "Maximum Principles for Discrete and Semidiscrete Reaction-Diffusion Equation." Discrete Dynamics in Nature and Society 2015 (2015): 1–13. http://dx.doi.org/10.1155/2015/791304.

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We study reaction-diffusion equations with a general reaction functionfon one-dimensional lattices with continuous or discrete timeux′ (or Δtux)=k(ux-1-2ux+ux+1)+f(ux),x∈Z. We prove weak and strong maximum and minimum principles for corresponding initial-boundary value problems. Whereas the maximum principles in the semidiscrete case (continuous time) exhibit similar features to those of fully continuous reaction-diffusion model, in the discrete case the weak maximum principle holds for a smaller class of functions and the strong maximum principle is valid in a weaker sense. We describe in detail how the validity of maximum principles depends on the nonlinearity and the time step. We illustrate our results on the Nagumo equation with the bistable nonlinearity.

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7

Radice, Teresa, and Gabriella Zecca. "The Maximum principle of Alexandrov for very weak solutions." Journal of Differential Equations 256, no. 3 (February 2014): 1133–50. http://dx.doi.org/10.1016/j.jde.2013.10.010.

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8

de Pinho, Maria do Rosário, and Achim Ilchmann. "Weak maximum principle for optimal control problems with mixed constraints." Nonlinear Analysis: Theory, Methods & Applications 48, no. 8 (March 2002): 1179–96. http://dx.doi.org/10.1016/s0362-546x(01)00094-3.

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9

Zhuge, Jinping. "Weak maximum principle for biharmonic equations in quasiconvex Lipschitz domains." Journal of Functional Analysis 279, no. 12 (December 2020): 108786. http://dx.doi.org/10.1016/j.jfa.2020.108786.

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10

Huang, Xueping. "Stochastic incompleteness for graphs and weak Omori–Yau maximum principle." Journal of Mathematical Analysis and Applications 379, no. 2 (July 2011): 764–82. http://dx.doi.org/10.1016/j.jmaa.2011.02.009.

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11

Ilter, Serkan. "Weak maximum principle for optimal control problems of nonsmooth systems." Applied Mathematics and Computation 218, no. 3 (October 2011): 805–8. http://dx.doi.org/10.1016/j.amc.2011.03.064.

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12

Gavrilov, A. A., and O. M. Penkin. "Weak maximum principle for elliptic operators on a stratified set." Journal of Mathematical Sciences 142, no. 3 (April 2007): 2079–84. http://dx.doi.org/10.1007/s10958-007-0117-2.

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13

Zhou, Shuqing, and Hui Li. "Maximum Principles for Dynamic Equations on Time Scales and Their Applications." Journal of Applied Mathematics 2014 (2014): 1–6. http://dx.doi.org/10.1155/2014/434582.

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We consider the second dynamic operators of elliptic type on time scales. We establish basic generalized maximum principles and apply them to obtain weak comparison principle for second dynamic elliptic operators and to obtain the uniqueness of Dirichlet boundary value problems for dynamic elliptic equations.

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14

Huang, Weizhang, and Yanqiu Wang. "Discrete Maximum Principle for the Weak Galerkin Method for Anisotropic Diffusion Problems." Communications in Computational Physics 18, no. 1 (July 2015): 65–90. http://dx.doi.org/10.4208/cicp.180914.121214a.

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AbstractA weak Galerkin discretization of the boundary value problem of a general anisotropic diffusion problem is studied for preservation of the maximum principle. It is shown that the direct application of the M-matrix theory to the stiffness matrix of the weak Galerkin discretization leads to a strong mesh condition requiring all of the mesh dihedral angles to be strictly acute (a constant-order away from 90 degrees). To avoid this difficulty, a reduced system is considered and shown to satisfy the discrete maximum principle under weaker mesh conditions. The discrete maximum principle is then established for the full weak Galerkin approximation using the relations between the degrees of freedom located on elements and edges. Sufficient mesh conditions for both piecewise constant and general anisotropic diffusion matrices are obtained. These conditions provide a guideline for practical mesh generation for preservation of the maximum principle. Numerical examples are presented.

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15

Asperó, David, and Philip D. Welch. "Bounded Martin's Maximum, weak Erdӧs cardinals, and ψAc." Journal of Symbolic Logic 67, no. 3 (September 2002): 1141–52. http://dx.doi.org/10.2178/jsl/1190150154.

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AbstractWe prove that a form of the Erdӧs property (consistent with V = L[Hω2] and strictly weaker than the Weak Chang's Conjecture at ω1), together with Bounded Martin's Maximum implies that Woodin's principle ψAC holds, and therefore . We also prove that ψAC implies that every function f: ω1 → ω1 is bounded by some canonical function on a club and use this to produce a model of the Bounded Semiproper Forcing Axiom in which Bounded Martin's Maximum fails.

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16

Bonafede, Salvatore. "A weak maximum principle and estimates of ${\rm ess}\sup\sb \Omega u$ for nonlinear degenerate elliptic equations." Czechoslovak Mathematical Journal 46, no. 2 (1996): 259–69. http://dx.doi.org/10.21136/cmj.1996.127289.

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17

Boccardo, Lucio. "Weak maximum principle for Dirichlet problems with convection or drift terms." Mathematics in Engineering 3, no. 3 (2021): 1–9. http://dx.doi.org/10.3934/mine.2021026.

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18

Leykekhman, Dmitriy, and Buyang Li. "Weak discrete maximum principle of finite element methods in convex polyhedra." Mathematics of Computation 90, no. 327 (July 27, 2020): 1–18. http://dx.doi.org/10.1090/mcom/3560.

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19

Albanese, Guglielmo, Luis Alías, and Marco Rigoli. "A general form of the weak maximum principle and some applications." Revista Matemática Iberoamericana 29, no. 4 (2013): 1437–76. http://dx.doi.org/10.4171/rmi/764.

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20

Valero, José. "A Weak Comparison Principle for Reaction-Diffusion Systems." Journal of Function Spaces and Applications 2012 (2012): 1–30. http://dx.doi.org/10.1155/2012/679465.

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We prove a weak comparison principle for a reaction-diffusion system without uniqueness of solutions. We apply the abstract results to the Lotka-Volterra system with diffusion, a generalized logistic equation, and to a model of fractional-order chemical autocatalysis with decay. Moreover, in the case of the Lotka-Volterra system a weak maximum principle is given, and a suitable estimate in the space of essentially bounded functionsL∞is proved for at least one solution of the problem.

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21

Capuzzo Dolcetta, Italo. "The weak maximum principle for degenerate elliptic equations: unbounded domains and systems." Mathematics in Engineering 2, no. 4 (2020): 772–86. http://dx.doi.org/10.3934/mine.2020036.

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22

Aseev, S. M., and V. M. Veliov. "Maximum principle for infinite-horizon optimal control problems under weak regularity assumptions." Proceedings of the Steklov Institute of Mathematics 291, S1 (December 2015): 22–39. http://dx.doi.org/10.1134/s0081543815090023.

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23

Arutyunov, A. V., D. Yu Karamzin, and F. L. Pereira. "Maximum principle in problems with mixed constraints under weak assumptions of regularity." Optimization 59, no. 7 (October 2010): 1067–83. http://dx.doi.org/10.1080/02331930903395832.

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24

Hilscher, Roman, and Vera Zeidan. "Weak maximum principle and accessory problem for control problems on time scales." Nonlinear Analysis: Theory, Methods & Applications 70, no. 9 (May 2009): 3209–26. http://dx.doi.org/10.1016/j.na.2008.04.025.

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25

Wang, Junping, Xiu Ye, Qilong Zhai, and Ran Zhang. "Discrete maximum principle for the P1−P0 weak Galerkin finite element approximations." Journal of Computational Physics 362 (June 2018): 114–30. http://dx.doi.org/10.1016/j.jcp.2018.02.013.

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26

Alías, Luis J., Juliana F. R. Miranda, and Marco Rigoli. "A new open form of the weak maximum principle and geometric applications." Communications in Analysis and Geometry 24, no. 1 (2016): 1–43. http://dx.doi.org/10.4310/cag.2016.v24.n1.a1.

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27

de Pinho, M. d. R., P. Loewen, and G. N. Silva. "A Weak Maximum Principle for Optimal Control Problems with Nonsmooth Mixed Constraints." Set-Valued and Variational Analysis 17, no. 2 (April 29, 2009): 203–21. http://dx.doi.org/10.1007/s11228-009-0108-1.

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28

Slavík, Antonín, Petr Stehlík, and Jonáš Volek. "Well-posedness and maximum principles for lattice reaction-diffusion equations." Advances in Nonlinear Analysis 8, no. 1 (March 17, 2017): 303–22. http://dx.doi.org/10.1515/anona-2016-0116.

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Abstract Existence, uniqueness and continuous dependence results together with maximum principles represent key tools in the analysis of lattice reaction-diffusion equations. In this paper, we study these questions in full generality by considering nonautonomous reaction functions, possibly nonsymmetric diffusion and continuous, discrete or mixed time. First, we prove the local existence and global uniqueness of bounded solutions, as well as the continuous dependence of solutions on the underlying time structure and on initial conditions. Next, we obtain the weak maximum principle which enables us to get the global existence of solutions. Finally, we provide the strong maximum principle which exhibits an interesting dependence on the time structure. Our results are illustrated by the autonomous Fisher and Nagumo lattice equations and a nonautonomous logistic population model with a variable carrying capacity.

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29

Lei, Yang, Shurong Li, Xiaodong Zhang, Qiang Zhang, and Lanlei Guo. "Optimal Control of Polymer Flooding Based on Maximum Principle." Journal of Applied Mathematics 2012 (2012): 1–20. http://dx.doi.org/10.1155/2012/987975.

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Polymer flooding is one of the most important technologies for enhanced oil recovery (EOR). In this paper, an optimal control model of distributed parameter systems (DPSs) for polymer injection strategies is established, which involves the performance index as maximum of the profit, the governing equations as the fluid flow equations of polymer flooding, and the inequality constraint as the polymer concentration limitation. To cope with the optimal control problem (OCP) of this DPS, the necessary conditions for optimality are obtained through application of the calculus of variations and Pontryagin’s weak maximum principle. A gradient method is proposed for the computation of optimal injection strategies. The numerical results of an example illustrate the effectiveness of the proposed method.

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30

Kim, Doyoon, and Seungjin Ryu. "The weak maximum principle for second-order elliptic and parabolic conormal derivative problems." Communications on Pure & Applied Analysis 19, no. 1 (2020): 493–510. http://dx.doi.org/10.3934/cpaa.2020024.

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31

Zhou, Huifang, Xiuli Wang, and Jiwei Jia. "Discrete maximum principle for the weak Galerkin method on triangular and rectangular meshes." Journal of Computational and Applied Mathematics 402 (March 2022): 113784. http://dx.doi.org/10.1016/j.cam.2021.113784.

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32

Li, Yusong, and Harry Zheng. "Weak Necessary and Sufficient Stochastic Maximum Principle for Markovian Regime-Switching Diffusion Models." Applied Mathematics & Optimization 71, no. 1 (May 7, 2014): 39–77. http://dx.doi.org/10.1007/s00245-014-9252-6.

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33

Liu, Xu, and Xu Zhang. "The weak maximum principle for a class of strongly coupled elliptic differential systems." Journal of Functional Analysis 263, no. 7 (October 2012): 1862–86. http://dx.doi.org/10.1016/j.jfa.2012.06.020.

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34

Drábek, Pavel. "On a maximum principle for weak solutions of some quasi-linear elliptic equations." Applied Mathematics Letters 22, no. 10 (October 2009): 1567–70. http://dx.doi.org/10.1016/j.aml.2009.04.005.

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35

Pilipović, Stevan, and Dora Seleši. "On the Generalized Stochastic Dirichlet Problem—Part I: The Stochastic Weak Maximum Principle." Potential Analysis 32, no. 4 (September 25, 2009): 363–87. http://dx.doi.org/10.1007/s11118-009-9155-3.

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36

Biswas, Anup, and József Lőrinczi. "Maximum principles for time-fractional Cauchy problems with spatially non-local components." Fractional Calculus and Applied Analysis 21, no. 5 (October 25, 2018): 1335–59. http://dx.doi.org/10.1515/fca-2018-0070.

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Abstract We show a strong maximum principle and an Alexandrov-Bakelman-Pucci estimate for the weak solutions of a Cauchy problem featuring Caputo time-derivatives and non-local operators in space variables given in terms of Bernstein functions of the Laplacian. To achieve this, first we propose a suitable meaning of a weak solution, show their existence and uniqueness, and establish a probabilistic representation in terms of time-changed Brownian motion. As an application, we also discuss an inverse source problem.

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37

Liu, Ximin, and Ning Zhang. "Spacelike Hypersurfaces in Weighted Generalized Robertson-Walker Space-Times." Advances in Mathematical Physics 2018 (2018): 1–6. http://dx.doi.org/10.1155/2018/4523512.

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Applying generalized maximum principle and weak maximum principle, we obtain several uniqueness results for spacelike hypersurfaces immersed in a weighted generalized Robertson-Walker (GRW) space-time under suitable geometric assumptions. Furthermore, we also study the special case when the ambient space is static and provide some results by using Bochner’s formula.

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38

Capuzzo-Dolcetta, I., F. Leoni, and A. Vitolo. "The Alexandrov-Bakelman-Pucci Weak Maximum Principle for Fully Nonlinear Equations in Unbounded Domains." Communications in Partial Differential Equations 30, no. 12 (November 2005): 1863–81. http://dx.doi.org/10.1080/03605300500300030.

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39

de Pinho, M. do R. "On the weak maximum principle for optimal control problems with state dependent control constraints." Nonlinear Analysis: Theory, Methods & Applications 30, no. 4 (December 1997): 2481–88. http://dx.doi.org/10.1016/s0362-546x(97)00332-5.

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40

Du, Yihong, and Zongming Guo. "Symmetry for elliptic equations in a half-space without strong maximum principle." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 134, no. 2 (April 2004): 259–69. http://dx.doi.org/10.1017/s0308210500003218.

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For a wide class of nonlinearities f(u) satisfying but not necessarily Lipschitz continuous, we study the quasi-linear equation where T = {x = (x1, x2, …, xN) ∈ RN: x1 > 0} with N ≥ 2. By using a new approach based on the weak maximum principle, we show that any positive solution on T must be a function of x1 only. Under our assumptions, the strong maximum principle does not hold in general and the solution may develop a flat core; our symmetry result allows an easy and precise determination of the flat core.

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41

A., Khafagy S. "Maximum Principle and Existence of Weak Solutions for Nonlinear System Involving Singular p-Laplacian Operators." Journal of Partial Differential Equations 29, no. 2 (June 2016): 89–101. http://dx.doi.org/10.4208/jpde.v29.n2.1.

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42

Liu, Yujie, and Junping Wang. "A discrete maximum principle for the weak Galerkin finite element method on nonuniform rectangular partitions." Numerical Methods for Partial Differential Equations 36, no. 3 (November 18, 2019): 552–78. http://dx.doi.org/10.1002/num.22440.

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43

Read, Randy J., and Airlie J. McCoy. "Maximum-likelihood determination of anomalous substructures." Acta Crystallographica Section D Structural Biology 74, no. 2 (February 1, 2018): 98–105. http://dx.doi.org/10.1107/s2059798317013468.

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A fast Fourier transform (FFT) method is described for determining the substructure of anomalously scattering atoms in macromolecular crystals that allows successful structure determination by X-ray single-wavelength anomalous diffraction (SAD). This method is based on the maximum-likelihood SAD phasing function, which accounts for measurement errors and for correlations between the observed and calculated Bijvoet mates. Proof of principle is shown that this method can improve determination of the anomalously scattering substructure in challenging cases where the anomalous scattering from the substructure is weak but the substructure also constitutes a significant fraction of the real scattering. The method is deterministic and can be fast compared with existing multi-trial dual-space methods for SAD substructure determination.

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44

Byszewski, Ludwik. "Impulsive nonlocal nonlinear parabolic differential problems." Journal of Applied Mathematics and Stochastic Analysis 6, no. 3 (January 1, 1993): 247–60. http://dx.doi.org/10.1155/s1048953393000206.

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The aim of the paper is to prove a theorem about a weak impulsive nonlinear parabolic differential inequality together with weak impulsive nonlocal nonlinear inequalities. A weak maximum principle for an impulsive nonlinear parabolic differential inequality together with weak impulsive nonlocal nonlinear inequalities and an uniqueness criterion for the existence of the classical solution of an impulsive nonlocal nonlinear parabolic differential problem are obtained as a consequence of the theorem about the weak impulsive nonlinear parabolic differential inequality together with weak impulsive nonlocal nonlinear inequalities.

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45

BERTHELIN, F. "EXISTENCE AND WEAK STABILITY FOR A PRESSURELESS MODEL WITH UNILATERAL CONSTRAINT." Mathematical Models and Methods in Applied Sciences 12, no. 02 (February 2002): 249–72. http://dx.doi.org/10.1142/s0218202502001635.

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We consider a two-phase model described by a pressureless gas system with unilateral constraint. We prove weak stability and the existence of weak solutions by passing to the limit in the sticky-blocks dynamics. We obtain the maximum principle on the velocity, the Oleinik entropy condition and local entropy inequalities. Initial data are taken in a very weak sense since the solution can jump initially in time.

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46

FUCHS, GUNTER. "HIERARCHIES OF FORCING AXIOMS, THE CONTINUUM HYPOTHESIS AND SQUARE PRINCIPLES." Journal of Symbolic Logic 83, no. 1 (March 2018): 256–82. http://dx.doi.org/10.1017/jsl.2017.46.

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AbstractI analyze the hierarchies of the bounded and the weak bounded forcing axioms, with a focus on their versions for the class of subcomplete forcings, in terms of implications and consistency strengths. For the weak hierarchy, I provide level-by-level equiconsistencies with an appropriate hierarchy of partially remarkable cardinals. I also show that the subcomplete forcing axiom implies Larson’s ordinal reflection principle atω2, and that its effect on the failure of weak squares is very similar to that of Martin’s Maximum.

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47

Náprstek, Jiří, and Cyril Fischer. "Maximum Entropy Probability Density Principle in Probabilistic Investigations of Dynamic Systems." Entropy 20, no. 10 (October 15, 2018): 790. http://dx.doi.org/10.3390/e20100790.

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In this study, we consider a method for investigating the stochastic response of a nonlinear dynamical system affected by a random seismic process. We present the solution of the probability density of a single/multiple-degree of freedom (SDOF/MDOF) system with several statically stable equilibrium states and with possible jumps of the snap-through type. The system is a Hamiltonian system with weak damping excited by a system of non-stationary Gaussian white noise. The solution based on the Gibbs principle of the maximum entropy of probability could potentially be implemented in various branches of engineering. The search for the extreme of the Gibbs entropy functional is formulated as a constrained optimization problem. The secondary constraints follow from the Fokker–Planck equation (FPE) for the system considered or from the system of ordinary differential equations for the stochastic moments of the response derived from the relevant FPE. In terms of the application type, this strategy is most suitable for SDOF/MDOF systems containing polynomial type nonlinearities. Thus, the solution links up with the customary formulation of the finite elements discretization for strongly nonlinear continuous systems.

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48

Andreani, Roberto, Valeriano Antunes de Oliveira, Jamielli Tomaz Pereira, and Geraldo Nunes Silva. "A weak maximum principle for optimal control problems with mixed constraints under a constant rank condition." IMA Journal of Mathematical Control and Information 37, no. 3 (February 5, 2020): 1021–47. http://dx.doi.org/10.1093/imamci/dnz036.

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Abstract Necessary optimality conditions for optimal control problems with mixed state-control equality constraints are obtained. The necessary conditions are given in the form of a weak maximum principle and are obtained under (i) a new regularity condition for problems with mixed linear equality constraints and (ii) a constant rank type condition for the general non-linear case. Some instances of problems with equality and inequality constraints are also covered. Illustrative examples are presented.

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49

Peligrad, Magda. "Maximum of partial sums and an invariance principle for a class of weak dependent random variables." Proceedings of the American Mathematical Society 126, no. 4 (1998): 1181–89. http://dx.doi.org/10.1090/s0002-9939-98-04177-x.

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50

Jurčišin, Miroslav, Marek Blažo, and Ján Slota. "Optical Investigation of Component Made by FDM Technology." Applied Mechanics and Materials 827 (February 2016): 69–72. http://dx.doi.org/10.4028/www.scientific.net/amm.827.69.

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3D printed plastic components are nowadays frequently used parts in all areas of industrial sphere. These components are often made by FDM technology. The main advantage of this technology is quick manufacturing process, price and also possibility of producing complex parts. This paper is aimed to the component made by FDM technology from the view of their strength. Specially designed chair was loaded by different force and the maximum load before destruction was measured. Chair was under inspection of two different optical strain measurement systems working on different principles. System PONTOS working on the principle of digital photogrammetry and system ARAMIS working on the principle of digital image correlation were used. These systems were used in order to investigate and identify weak places of this chair.

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