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

Tom 81 / 2008

Todor Gramchev, Grzegorz /Lysik Banach Center Publications 81 (2008), 213-226 MSC: Primary 35B65, 35E15, 35K05, 35K15. DOI: 10.4064/bc81-0-14

Streszczenie

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.

Autorzy

  • Todor GramchevDipartimento di Matematica e Informatica
    Università di Cagliari
    via Ospedale 72
    09124 Cagliari, Italy
    e-mail
  • Grzegorz /LysikInstitute of Mathematics
    Polish Academy of Sciences
    Śniadeckich 8
    00-956 Warszawa 10, Poland
    and
    Świ/etokrzyska Academy, Kielce, Poland
    e-mail

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