Existence of solutions for a fractional semilinear parabolic equation with singular initial data. (October 2018) - Hisa, Kotaro; Ishige, Kazuhiro
Abstract: In this paper we obtain necessary conditions and sufficient conditions on the initial data for the solvability of the Cauchy problem ∂ t u + ( − Δ ) θ 2 u = u p, x ∈ R N, t > 0, u ( 0 ) = μ ≥ 0 in R N, where N ≥ 1, 0 < θ ≤ 2, p > 1 and μ is a Radon measure or a measurable function in R N . Our conditions lead optimal estimates of the life span of the solution with μ behaving like λ | x | − A ( A > 0 ) at the space infinity, as λ → + 0 .