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

Todor Gramchev, Grzegorz Łysik (2008)

Banach Center Publications

We study the Gevrey regularity down to t = 0 of solutions to the initial value problem for a semilinear heat equation t u - Δ 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 ≥ 0 and x ∈ ℝⁿ for some conservative nonlinear terms with symmetries.

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