A Lyapunov function for fully nonlinear parabolic equations in one spatial variable
Dynamical Systems
2020-12-16 v3 Analysis of PDEs
Abstract
Lyapunov functions are used to prove stability of equilibria, or to indicate a gradient-like structure of a dynamical system. Zelenyak (1968) and Matano (1988) constructed a Lyapunov function for quasilinear parabolic equations. We modify Matano's method to construct a Lyapunov function for fully nonlinear parabolic equations under Dirichlet and mixed nonlinear boundary conditions of Robin type.
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Cite
@article{arxiv.1802.09754,
title = {A Lyapunov function for fully nonlinear parabolic equations in one spatial variable},
author = {Phillipo Lappicy and Bernold Fiedler},
journal= {arXiv preprint arXiv:1802.09754},
year = {2020}
}
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9 pages