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NCTS Webinar on Nonlinear Evolutionary Dynamics
 
9:00 - 10:30, October 19, 2021 (Tuesday)
Cisco Webex, Online seminar
(線上演講 Cisco Webex)
An Energy Formula for Fully Nonlinear Parabolic PDEs in One Spatial Dimension
Phillipo Lappicy (Universidade de São Paulo)

Abstract:

Besides the classical questions of existence and regularity of partial differential equations (PDEs), energy (or Lyapunov) functions can also be used in order to prove stability of equilibria, or to indicate a gradient-like structure of a dynamical system. Matano (1988) constructed a Lyapunov function for quasilinear non-degenerate parabolic equations with gradient dependency. We modify Matano's method to construct an energy formula for fully nonlinear parabolic PDEs of non-degenerate or degenerate type with Dirichlet or nonlinear Robin boundary conditions. This is based on joint explorations with B. Fiedler and E. Beatriz.

 

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Meeting number (access code): 2512 886 1903
Meeting password: tPJQqt2bR44 (87577822 from phones and video systems)


 

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