We study the Gevrey regularity down to t = 0 of solutions to the initial value problem for a semilinear heat equation . The approach is based on suitable iterative fixed point methods in based Banach spaces with anisotropic Gevrey norms with respect to the time and the space variables. We also construct explicit solutions uniformly analytic in t ≥ 0 and x ∈ ℝⁿ for some conservative nonlinear terms with symmetries.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-bc81-0-14,
author = {Todor Gramchev and Grzegorz \L ysik},
title = {Uniform analytic-Gevrey regularity of solutions to a semilinear heat equation},
journal = {Banach Center Publications},
volume = {83},
year = {2008},
pages = {213-226},
zbl = {1172.35342},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc81-0-14}
}
Todor Gramchev; Grzegorz Łysik. Uniform analytic-Gevrey regularity of solutions to a semilinear heat equation. Banach Center Publications, Tome 83 (2008) pp. 213-226. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc81-0-14/