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A Lyapunov function for fully nonlinear parabolic equations in one spatial variable. (arXiv:1802.09754v2 [math.DS] UPDATED)

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.查看全文

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