Cauchy problem, Comparison principle
In this paper we get estimates of life span of a Cauchy problem ut(x, t) = ∆ u(x, t) +u(x, t)p, x∈Rn, t >0,u(x,0) =λφ(x), x∈Rn in terms of the positive constant parameterλ whenφ(x)∈Lq is a nonnegative bounded continuous function in Rn but not identically zero, where q is large enough. The technique we used in this paper is the Comparison Principle.
International Journal of Pure and Applied Mathematics
Hyuk Kang, Joon, "Estimates of Life Span of Solutions of a Cauchy Problem" (2017). Faculty Publications. 707.
Retrieved August 24, 2018 from https://ijpam.eu/contents/2017-116-3/9/9.pdf