An energy formula for fully nonlinear degenerate parabolic equations in one spatial dimension

2022/01/11 by Lappicy, Phillipo, Beatriz, Ester · 1 citation
#35A15 #35A16 #35B38 #35K65 #37L45 #Analysis of PDEs (math.AP) #Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.2201.04215

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.

Cited by

• Real-time blow-up and connection graphs of rational vector fields on the Riemann sphere

Related

• A Lyapunov function for fully nonlinear parabolic equations in one spatial variable
• Existence of solutions to degenerate parabolic equations via the Monge-Kantorovich theory
• Classification of connecting solutions of semilinear parabolic equations
• On two coupled degenerate parabolic equations motivated by thermodynamics
• Decay of periodic entropy solutions to degenerate nonlinear parabolic equations