09/09/2022, 15:00 — 15:45 — Abreu Faro Amphitheatre
Carlos Rocha, Instituto Superior Técnico, Universidade de Lisboa

Order Preserving Semiflows Revisited

Dynamical systems generated by scalar reaction-diffusion equations enjoy special properties that lead to a very simple structure for the semiflow. Among these properties, the monotone behavior of the number of zeros of the solutions plays an essential role. This discrete Lyapunov functional, the zero number, contains important information on the spectral behavior of the linearization and leads to the simple description of the dynamical system.

Other systems possess this kind of discrete Lyapunov functional and we review some classes of linear equations that generate semiflows with this property. Moreover, we ask if this property is characteristic of such problems.

This is based on a joint work with Giorgio Fusco.

See also

ISTIME2022 CRocha.pdf