Wednesday, January 28, 2009. Minnesota PDE seminar

Speaker: Professor Peter Polacik, University of Minnesota.

Title:   Parabolic Liouville theorems and their applications.

Abstract:  Parabolic Liouville theorems state that if u is an entire solution of a specific parabolic equation 
(semilinear heat equation with power nonlinearity) and u is contained in an admissible class of functions, 
then u is necessarily the trivial solution. After a discussion of available Liouville theorems for nonnegative solutions, 
we shall focus on a Liouville theorem for radial sign-changing solutions. Among applications, 
we shall mention universal a priori estimates of solutions and a construction of infinitely 
many periodic solutions of periodic-parabolic boundary value problems.

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