Degenerate gradient systems: the bidomain problem and Dirichlet-to-Neumann operators

Abstract: We identify a common structure behind several parabolic PDE models involving Dirichlet-to-Neumann operators, the bidomain operator, and some more, and we show that they actually have a gradient structure, possibly up to lower order perturbations. This has consequences for wellposedness of these PDEs, regularity of solutions and their asymptotic behaviour.

Mathematics

Audience: researchers in the topic

Necas PDE seminar