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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm147-2-6,
author = {Zoran Gruji\'c},
title = {Dynamics of complex singularities in 1D nonlinear parabolic PDE's},
journal = {Studia Mathematica},
volume = {147},
year = {2001},
pages = {183-195},
zbl = {0984.30030},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm147-2-6}
}
Zoran Grujić. Dynamics of complex singularities in 1D nonlinear parabolic PDE's. Studia Mathematica, Tome 147 (2001) pp. 183-195. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm147-2-6/