Asymptotics for a nonlinear integral equation with a generalized heat kernel

Kazuhiro Ishige, Tatsuki Kawakami, Kanako Kobayashi

This paper is concerned with a nonlinear integral equation $$(P)u(x,t)={\int }_{{\mathbf{R}}^N}G(x-y,t)\phi (y)dy+{\int }_0^t{\int }_{{\mathbf{R}}^N}G(x-y,t-s)f(y,s:u)dyds,$$ where $N\ge 1…