Local asymptotics for solutions to Heat equations with inverse-square potentials
Ana Primo,
(Instituto de Ciencias Matemáticas - CSIC Madrid)
Miercoles 6 de abril 2011
Parabolic problems with singular inverse square potentials arise in the linearization of standard
combustion models. The properties of the heat operator are strongly affected by the presence
of the singularity. In this talk, the aim is to describe the exact behavior near the singularity
of solutions to linear and subcritical semilinear parabolic equations with Hardy type potentials.
By combining a parabolic Almgren type monotonicity formula with blow-up methods, a precise
description in terms of the eigenvalues and eigenfunctions of the perturbed Orstein-Uhlenbeck
operator is obtained. Moreover, as a byproduct, a unique continuation property is deduced.