Prof. Peter Polacik, Univ of Minnesota
Time and Venue:
2:10pm, Tuesday (31 May, 2011), Access Grid Room in the ITD
Exponential separation between positive and sign-changing solutions and its
application in studies of threshold solutions of nonlinear parabolic
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.