Exponential separation between positive and sign-changing solutions of parabolic equations and its applications

Thursday, May 2, 2013 - 10:30am - 12:00pm
Lind 305
Peter Polacik (University of Minnesota, Twin Cities)
In linear nonautonomous second-order parabolic equations, the exponential separation refers to the exponential decay of any sign-changing solution relative to any positive solution. In this lecture, we first summarize key results on the exponential separation and related concepts, the principal Floquet bundle and principal Lyapunov exponent. Then we show how they can be effectively used in studies of some nonlinear parabolic problems on $R^N$. In particular, we shall discuss the instability of localized solutions, and a Liouville-type theorem for radial solutions.