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

In this paper we obtain necessary conditions and sufficient conditions on the initial data for the solvability of the Cauchy problem ∂tu+(−Δ)θ2u=up,x∈RN,t>0,u(0)=μ≥0 in RN,where N≥1, 01 and μ is a Radon measure or a measurable function in RN. Our conditions lead optimal estimates of the life span...

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Bibliographic Details
Published in:Nonlinear analysis 2018-10, Vol.175, p.108-132
Main Authors: Hisa, Kotaro, Ishige, Kazuhiro
Format: Article
Language:English
Subjects:
Cauchy problems
Mathematical functions
Mathematicians
Parabolas
Radon
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Summary:In this paper we obtain necessary conditions and sufficient conditions on the initial data for the solvability of the Cauchy problem ∂tu+(−Δ)θ2u=up,x∈RN,t>0,u(0)=μ≥0 in RN,where N≥1, 01 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.
ISSN:0362-546X
1873-5215
DOI:10.1016/j.na.2018.05.011