## Dynamics, Geometry, & Groups Seminar

### Friday, February 7th, 2020

**Time:** 10:30 a.m** Place:** Jeffery Hall 319

**Speaker:** Giusy Mazzone (Queen's University)

**Title:** On the stability of solutions to semilinear evolution equations.

**Abstract:** In this talk, we will discuss the stability and long-time behavior of solutions to nonlinear evolution equations in Banach spaces. We are particularly interested in semilinear parabolic systems of PDEs possessing a nontrivial manifold of equilibria, and whose linearization admits zero as a semi-simple eigenvalue. We will provide sufficient conditions that ensure asymptotic (exponential) stability of equilibria. We will also discuss an instability result for normally hyperbolic equilibria, and provide conditions for their attainability. Applications to fluid-solid interaction problems will be presented.