Existence of solutions for a fractional semilinear parabolic equation with singular initial data. (October 2018)

• Record Type: Journal Article
• Authors: Hisa, Kotaro; Ishige, Kazuhiro
• Is Part Of: Nonlinear analysis. Volume 175(2018)
• Page Start: 108
• Page End: 132
• Publication Date: 2018-10
• Subjects: Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2018.05.011
• Languages: English
• ISSNs: 0362-546X

Abstract

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 .