Uniform analytic-Gevrey regularity of solutions to a semilinear heat equation

Todor Gramchev, and Grzegorz Łysik. "Uniform analytic-Gevrey regularity of solutions to a semilinear heat equation." Banach Center Publications 81.1 (2008): 213-226. <http://eudml.org/doc/282415>.

@article{TodorGramchev2008,
abstract = {We study the Gevrey regularity down to t = 0 of solutions to the initial value problem for a semilinear heat equation $∂_tu - Δu = u^M$. The approach is based on suitable iterative fixed point methods in $L^p$ 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.},
author = {Todor Gramchev, Grzegorz Łysik},
journal = {Banach Center Publications},
keywords = {semilinear heat equation; initial value problem; anisotropic Gevrey spaces},
language = {eng},
number = {1},
pages = {213-226},
title = {Uniform analytic-Gevrey regularity of solutions to a semilinear heat equation},
url = {http://eudml.org/doc/282415},
volume = {81},
year = {2008},
}

TY - JOUR
AU - Todor Gramchev
AU - Grzegorz Łysik
TI - Uniform analytic-Gevrey regularity of solutions to a semilinear heat equation
JO - Banach Center Publications
PY - 2008
VL - 81
IS - 1
SP - 213
EP - 226
AB - We study the Gevrey regularity down to t = 0 of solutions to the initial value problem for a semilinear heat equation $∂_tu - Δu = u^M$. The approach is based on suitable iterative fixed point methods in $L^p$ 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.
LA - eng
KW - semilinear heat equation; initial value problem; anisotropic Gevrey spaces
UR - http://eudml.org/doc/282415
ER -