TY - JOUR
T1 - Existence of solutions for a fractional semilinear parabolic equation with singular initial data
AU - Hisa, Kotaro
AU - Ishige, Kazuhiro
N1 - Funding Information:
The authors of this paper thank Professor Marek Fila for his useful comments on Corollary 1.1 . The second author of this paper was supported by the Grant-in-Aid for Scientific Research (A) (No. 15H02058 ), from Japan Society for the Promotion of Science .
Publisher Copyright:
© 2018 Elsevier Ltd
PY - 2018/10
Y1 - 2018/10
N2 - 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.
AB - 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.
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U2 - 10.1016/j.na.2018.05.011
DO - 10.1016/j.na.2018.05.011
M3 - Article
AN - SCOPUS:85048304588
SN - 0362-546X
VL - 175
SP - 108
EP - 132
JO - Nonlinear Analysis, Theory, Methods and Applications
JF - Nonlinear Analysis, Theory, Methods and Applications
ER -