About this Event
Speaker: Professor Peter Polacik (University of Minnesota)
Title: Large-time behavior of solutions of semilinear parabolic equations on the real line with convergent initial data
Abstract: The large-time behavior of bounded solutions of reaction-diffusion equations on the entire space, even in one dimension, is still far from being completely understood. In this talk, based on joint work with Antoine Pauthier, we will examine a specific class of solutions on the real line, namely solutions whose initial data have finite limits at infinity. We give nearly optimal conditions on such initial data which guarantee that the corresponding solution is quasiconvergent, that is, all its locally uniform limit profiles as time approaches infinity are steady states. Key results of this research and basic ingredients of the proofs will be discusse