Differential and Integral Equations

Sharp analytic-Gevrey regularity estimates down to $t=0$ for solutions to semilinear heat equations

Todor Gramchev and Grzegorz Łysik

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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.

Article information

Differential Integral Equations, Volume 21, Number 7-8 (2008), 771-799.

First available in Project Euclid: 20 December 2012

Permanent link to this document

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35K55: Nonlinear parabolic equations
Secondary: 35A20: Analytic methods, singularities 35B65: Smoothness and regularity of solutions 35K15: Initial value problems for second-order parabolic equations


Gramchev, Todor; Łysik, Grzegorz. Sharp analytic-Gevrey regularity estimates down to $t=0$ for solutions to semilinear heat equations. Differential Integral Equations 21 (2008), no. 7-8, 771--799. https://projecteuclid.org/euclid.die/1356038622

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