Gradient bounds for nonlinear degenerate parabolic equations and application to large time behavior of systems
Analysis of PDEs
2015-05-22 v2
Abstract
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.
Keywords
Cite
@article{arxiv.1407.3116,
title = {Gradient bounds for nonlinear degenerate parabolic equations and application to large time behavior of systems},
author = {Olivier Ley and Vinh Duc Nguyen},
journal= {arXiv preprint arXiv:1407.3116},
year = {2015}
}