Existence and non-existence of a fast diffusion equation in R-n

[摘要] In this paper we study the global existence and asymptotic behaviour of solutions to u(1)=Delta log u for the Cuachy initial value problem in R-n. We prove that if n greater than or equal to 3. then every solution satisfies integral(Rn)u(p)(x, t)dx = infinity for any 1 n/2. Hence, we extend a previous result of Vazquez [19] which claims that integral(Rn)udx=infinity for 0<1(max). (C) 1997 Academic Press.

[发布日期] 1997-05-20