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

• Autorzy: Todor Gramchev , Grzegorz Łysik
• Języki publikacji: EN

Abstrakty

EN

We study the Gevrey regularity down to t = 0 of solutions to the initial value problem for a semilinear heat equation $∂_tu - Δu = u^M$. 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.

Kategorie tematyczne

• 35K05: Heat equation
• 35K15: Initial value problems for second-order parabolic equations
• 35E15: Initial value problems
• 35B65: Smoothness and regularity of solutions

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 2008
• Tom: 81
• Numer: 1
• Strony: 213-226

Daty

wydano

2008

Twórcy

autor

Todor Gramchev

• Dipartimento di Matematica e Informatica, Università di Cagliari, via Ospedale 72, 09124 Cagliari, Italy

autor

Grzegorz Łysik

• Institute of Mathematics, Polish Academy of Sciences, Śniadeckich 8, 00-956 Warszawa 10, Poland
• Świętokrzyska Academy, Kielce, Poland

Identyfikatory

DOI

10.4064/bc81-0-14