Gradient bounds for nonlinear degenerate parabolic equations and application to large time behavior of systems

被引：12

作者：

Ley, Olivier ^{[1
]}

Nguyen, Vinh Duc ^{[2
]}

机构：

[1] INSA Rennes, IRMAR, F-35708 Rennes, France

[2] Univ Paris Est Creteil, LAMA, F-94010 Creteil, France

来源：

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2016年 / 130卷

关键词：

Nonlinear degenerate parabolic equations; Nonlinear degenerate elliptic equations; Hamilton-Jacobi equations; Monotone systems; Gradient bounds; Oscillation; Strong maximum principle; Ergodic problem; Asymptotic behavior; Viscosity solutions; WEAKLY COUPLED SYSTEMS; HAMILTON-JACOBI EQUATIONS; VISCOSITY SOLUTIONS; DYNAMICAL-APPROACH; GROWTH; PDE;

D O I：

10.1016/j.na.2015.09.012

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We obtain new oscillation and gradient bounds for the viscosity solutions of fully nonlinear degenerate elliptic equations where the Hamiltonian is a sum of a sublinear and a superlinear part in the sense of Barles and Souganidis (2001). We use these bounds to study the asymptotic behavior of weakly coupled systems of fully nonlinear parabolic equations. Our results apply to some "asymmetric systems" where some equations contain a sublinear Hamiltonian whereas the others contain a superlinear one. Moreover, we can deal with some particular case of systems containing some degenerate equations using a generalization of the strong maximum principle for systems. (C) 2015 Elsevier Ltd. All rights reserved.

引用

页码：76 / 101

页数：26

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