Electron. J. Diff. Equ., Vol. 2013 (2013), No. 228, pp. 1-12.

Asymptotic behavior of solutions to parabolic problems with nonlinear nonlocal terms

Miguel Loayza

Abstract:
We study the existence and asymptotic behavior of self-similar solutions to the parabolic problem
$$ u_t-\Delta u=\int_0^t k(t,s)|u|^{p-1}u(s)ds\quad\hbox{on } (0,\infty)\times \mathbb{R}^N, $$
with p>1 and $u(0,\cdot) \in C_0(\mathbb{R}^N)$.

Submitted August 9, 2012. Published October 16, 2013.
Math Subject Classifications: 35K15, 35B40, 35E15.
Key Words: Nonlocal parabolic equation; global solution; self-similar solution.

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Miguel Loayza
Departamento de Matemática
Universidade Federal de Pernambuco
50740-540, Recife, PE, Brazil
email: miguel@dmat.ufpe.br

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