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Energy (or Lyapunov) functions are used to prove stability of equilibria, orto indicate a gradient-like structure of a dynamical system. Matano constructeda Lyapunov function for quasilinear non-degenerate parabolic equations. Wemodify Matano's method to construct an energy formula for fully nonlineardegenerate parabolic equations. We provide several examples of formulae, and inparticular, a new energy candidate for the porous medium equation.

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