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2008 Sharp analytic-Gevrey regularity estimates down to $t=0$ for solutions to semilinear heat equations
Todor Gramchev, Grzegorz Łysik
Differential Integral Equations 21(7-8): 771-799 (2008).

Abstract

We study the Gevrey regularity down to $t=0$ of solutions to the initial-value problem for the semilinear heat equation $\partial_tu-\Delta u+F[u]=0$ with polynomial non-linearities. 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 space variables. We also construct explicit solutions uniformly analytic in $t\geq 0$ and $x\in {\mathbb R}^n$ for some conservative non-linear terms with symmetries.

Citation

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Todor Gramchev. Grzegorz Łysik. "Sharp analytic-Gevrey regularity estimates down to $t=0$ for solutions to semilinear heat equations." Differential Integral Equations 21 (7-8) 771 - 799, 2008.

Information

Published: 2008
First available in Project Euclid: 20 December 2012

zbMATH: 1224.35213
MathSciNet: MR2479691

Subjects:
Primary: 35K55
Secondary: 35A20, 35B65, 35K15

Rights: Copyright © 2008 Khayyam Publishing, Inc.

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Vol.21 • No. 7-8 • 2008
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