Non-uniqueness of the positive Cauchy problem for parabolic equations

[摘要] Given a real-valued function V on R '', we investigate how V determines whether uniqueness of nonnegative solutions of the Cauchy problem (partial derivative(r) - Delta(x) + V(x)) u(x, t) = 0 in R '' x (0, T), u(x, 0) = u(0)(x) holds or not. Necessary and sufficient conditions for the uniqueness to hold are given. (C) 1995 Academic Press, Inc.

[发布日期] 1995-12-10