Electronic Journal of Differential Equations,
Vol. 2013 (2013), No. 228, pp. 1-12.
Title: Asymptotic behavior of solutions to parabolic problems with nonlinear
nonlocal terms
Author: Miguel Loayza (Univ. Federal de Pernambuco, Recife, Brazil)
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.