3 papers
math.DS2020
Meanders, zero numbers and the cell structure of Sturm global attractors
Carlos Rocha, Bernold Fiedler
We study global attractors of semiflows generated by semilinear partial parabolic differential equations of the form ,…
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
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…