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Existence and nonexistence of positive solutions to a fractional par- abolic problem with singular weight at the boundary

Abstract : We consider the problem (P) u_t + (−∆)^ s u = λ \frac{u^p }{δ^{2s} (x) } in Ω T ≡ Ω × (0, T), u(x, 0) = u 0 (x) in Ω, u = 0 in (IR N \ Ω) × (0, T), where Ω ⊂ IR^ N is a bounded regular domain (in the sense that ∂Ω is of class C^{ 0,1}), δ(x) = dist(x, ∂Ω), 0 < s < 1, p > 0, λ > 0. The purpose of this work is twofold. First We analyze the interplay between the parameters s, p and λ in order to prove the existence or the nonexistence of solution to problem (P) in a suitable sense. This extends previous similar results obtained in the local case s = 1. Second We will especially point out the differences between the local and nonlocal cases.
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https://hal.univ-lorraine.fr/hal-03276139
Contributor : El Haj Laamri <>
Submitted on : Thursday, July 1, 2021 - 5:27:36 PM
Last modification on : Saturday, July 3, 2021 - 3:33:10 AM

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Boumediene Abdellaoui, Kheireddine Biroud, El-Haj Laamri. Existence and nonexistence of positive solutions to a fractional par- abolic problem with singular weight at the boundary. Journal of Evolution Equations, Springer Verlag, 2021, 21 (2), pp.1227-1261. ⟨10.1007/s00028-020-00623-9⟩. ⟨hal-03276139⟩

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