%0 Journal Article
%T Asymptotics for a nonlinear integral equation with a generalized heat kernel
%A Kazuhiro Ishige
%A Tatsuki Kawakami
%A Kanako Kobayashi
%J Mathematics
%D 2013
%I arXiv
%R 10.1007/s00028-014-0237-3
%X This paper is concerned with a nonlinear integral equation $$ (P)\qquad u(x,t)=\int_{{\bf R}^N}G(x-y,t)\varphi(y)dy+\int_0^t\int_{{\bf R}^N}G(x-y,t-s)f(y,s:u)dyds, \quad $$ where $N\ge 1$, $\varphi\in L^\infty({\bf R}^N)\cap L^1({\bf R}^N,(1+|x|^K)dx)$ for some $K\ge 0$. Here $G=G(x,t)$ is a generalization of the heat kernel. We are interested in the asymptotic expansions of the solution of $(P)$ behaving like a multiple of the integral kernel $G$ as $t\to\infty$.
%U http://arxiv.org/abs/1309.7118v1