Existence of solutions for a fractional semilinear parabolic equation with singular initial data

Kotaro Hisa, Kazuhiro Ishige

Research output: Contribution to journalArticlepeer-review

9 Citations (Scopus)

Abstract

In this paper we obtain necessary conditions and sufficient conditions on the initial data for the solvability of the Cauchy problem ∂tu+(−Δ)[Formula presented]u=up,x∈RN,t>0,u(0)=μ≥0 in RN,where N≥1, 0<θ≤2, p>1 and μ is a Radon measure or a measurable function in RN. 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.

Original languageEnglish
Pages (from-to)108-132
Number of pages25
JournalNonlinear Analysis, Theory, Methods and Applications
Volume175
DOIs
Publication statusPublished - 2018 Oct

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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