Title: Spatial Dynamics and Concatenated Wave Patterns
Speaker: Xiao-Biao Lin (North Carolina State)
Abstract: We consider a reaction-diffusion equation in one space dimension whose initial condition is approximately a sequence of widely separated traveling waves with increasing velocity, each of which is individually asymptotically stable. We show that the sequence of traveling waves is itself asymptotically stable: as t goes to infinity, the solution approaches the concatenated wave pattern, with different shifts of each wave allowed. Essentially the same result was proved by Beyn, Selle, Thümmler, and Wright. They regarded the concatenated wave pattern as a sum of traveling waves. On the contrary, we regard the pattern as a sequence of traveling waves restricted to subintervals of R and separated by small jump discontinuities.
Seminar URL: https://research.math.osu.edu/pde/
