**Mathematics Seminar**

Speaker:

Prof. Peter Polacik, Univ of Minnesota

Time and Venue:

2:10pm, Tuesday (31 May, 2011), Access Grid Room in the ITD

Title:

Exponential separation between positive and sign-changing solutions and its

application in studies of threshold solutions of nonlinear parabolic

equations

Abstract:

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 time-autonoumous parabolic problems,

this property is closely related to properties of the principal eigenvalue

and eigenfunction of the corresponding elliptic operator.

In this lecture, after summarizing key results on exponential separation,

we shall show how it can be effectively used in studies of nonlinear

parabolic problems. In particular, we shall discuss sharp transitions from

extinction to propagation (or blowup) for a class of semilinear parabolic

equations on R^N.