174 citations · 341 across the 19 of their papers we have counts for
Showing 2018Show all
3 papers · 1 filter
math.DS2018
Boundary orders and geometry of the signed Thom-Smale complex for Sturm global attractors
Bernold Fiedler, Carlos Rocha
We embark on a detailed analysis of the close relations between combinatorial and geometric aspects of the scalar parabolic PDE \begin{equation}\label{eq:*} u_t = u_{xx} + f(x,u,u_…
math.DS2018★ 12 cited
An explicit Lyapunov function for reflection symmetric parabolic partial differential equations on the circle
Bernold Fiedler, Clodoaldo Grotta-Ragazzo, Carlos Rocha
We construct an explicit Lyapunov function for scalar parabolic reaction-advection-diffusion equations under periodic boundary conditions. We assume the nonlinearity is even in the…
math.DS2018
A Lyapunov function for fully nonlinear parabolic equations in one spatial variable
Phillipo Lappicy, Bernold Fiedler
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 Lyapun…