Asymptotics for a nonlinear integral equation with a generalized heat kernel

作者：Ishige Kazuhiro^*; Kawakami Tatsuki; Kobayashi Kanako

来源：Journal of Evolution Equations, 2014, 14(4-5): 749-777.

DOI：10.1007/s00028-014-0237-3

This paper is concerned with a nonlinear integral equation (P) u(x, t) = integral (N)(R) G(x - y, t) phi(y)dy + integral(t)(0) integral(N)(R) G(x - y, t - s)f(y, s : u)dyds, %26lt;br%26gt;Where N %26gt;= 1, phi is an element of L-infinity (R-N) boolean AND L-1(R-N, (1+vertical bar x vertical bar(K))dx for some K %26gt;= 0. Hence, G = G(x, t) is phi 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 -%26gt; infinity.

• 出版日期2014-12