### PDE and Differential Geometry’ Seminar Existence of standing pulse solutions to a skew-gradient system Jieun Lee(UCONN)

Monday, October 28, 2019
2:30pm – 3:30pm

Storrs Campus
MONT 214

Reaction-diffusion systems have been primary tools for studying pattern formation. A skew-gradient system generalizes an important class of activator-inhibitor type reaction-diffusion systems that exhibit localized patterns such as fronts and pulses. In this talk we study the standing pulse solutions to a skew-gradient system of the form $u_t = du_{xx} + f(u) - v, \quad \quad v_t= v_{xx} - \gamma v - v^3 + u,$ on the domain $(-\infty, \infty)$. Using a variational approach, we establish the existence of standing pulse solutions with a sign change. In addition, we explore some qualitative properties of the standing pulse solutions.

Contact:

lihan.wang@uconn.edu

PDE and Differential Geometry Seminar (primary), UConn Master Calendar