Exponential separation between positive and sign-changing solutions and its application in studies of threshold solutions of nonlinear parabolic equations

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.