Dynamics of complex singularities in 1D nonlinear parabolic PDE's
Volume 147 / 2001
Studia Mathematica 147 (2001), 183-195
MSC: 30H05, 35B65.
DOI: 10.4064/sm147-2-6
Abstract
We establish local-in-time smoothing of a simple model nonlinear parabolic PDE in a scale of weighted Bergman spaces on a strip provided the weights are not too singular. This constitutes a very strong smoothing property since an immediate consequence is that the PDE can “push away” an algebraic-type complex singularity provided that the order of the singularity is small enough.
