NONLINEAR VOLTERRA-EQUATIONS OF PARABOLIC TYPE DUE TO SINGULAR KERNELS

[摘要] Sufficient conditions for the global existence of a strong solution of the equation u(t)(t, x) = integral-t/0k(t - s) sigma(u(x)(s, x)), ds + f(t, x) are given. The kernel k is nonincreasing and convex with lim inf(t down 0) square-root tk(t)>0, and sigma is increasing with 0 < inf sigma'(p) less-than-or-equal-to sup sigma(p) < infinity. Sufficiently smooth solutions are shown to be unique. (C) 1994 Academic Press. Inc.

[发布日期] 1994-08-01