An energy formula for fully nonlinear degenerate parabolic equations in one spatial dimension
Analysis of PDEs
2023-10-24 v2 Dynamical Systems
Abstract
Energy (or Lyapunov) functions are used to prove stability of equilibria, or to indicate a gradient-like structure of a dynamical system. Matano constructed a Lyapunov function for quasilinear non-degenerate parabolic equations. We modify Matano's method to construct an energy formula for fully nonlinear degenerate parabolic equations. We provide several examples of formulae, and in particular, a new energy candidate for the porous medium equation.
Keywords
Cite
@article{arxiv.2201.04215,
title = {An energy formula for fully nonlinear degenerate parabolic equations in one spatial dimension},
author = {Phillipo Lappicy and Ester Beatriz},
journal= {arXiv preprint arXiv:2201.04215},
year = {2023}
}
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19 pages