Uniform analytic-Gevrey regularity of solutions to a semilinear heat equation
Volume 81 / 2008
Banach Center Publications 81 (2008), 213-226
MSC: Primary 35B65, 35E15, 35K05, 35K15.
DOI: 10.4064/bc81-0-14
Abstract
We study the Gevrey regularity down to $t=0$ of solutions to the initial value problem for a semilinear heat equation $\partial_tu-\Delta u=u^M$. 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 $t\geq 0$ and $x\in \mathbb R^n$ for some conservative nonlinear terms with symmetries.
