English

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.

Keywords

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}
}

Comments

9 pages

R2 v1 2026-06-23T00:34:45.005Z