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arXiv · 1802.09754

A Lyapunov function for fully nonlinear parabolic equations in one spatial variable

Phillipo Lappicy·Bernold Fiedler
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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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Phillipo Lappicy, Bernold Fiedler. 2018-02-27. A Lyapunov function for fully nonlinear parabolic equations in one spatial variable. https://arxiv.org/abs/1802.09754

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