Decay at infinity for solutions to some fractional parabolic equations

2023/07/20 by Banerjee, Agnid, Ghosh, Abhishek
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2307.10887

Abstract

For s ∈ [1/2, 1), let u solve (∂_t - Δ)^s u = Vu in \mathbb Rⁿ × [-T, 0] for some T>0 where ||V|| _{C²(\mathbb Rⁿ × [-T, 0])} < ∞. We show that if for some 0< c< T and ε>0 (1)/(c) ∫_[-c,0] u²(x, t) dt ≤ Ce^-|x|^2+ε ∀ x ∈ \mathbb Rⁿ, then u ≡ 0 in \mathbb Rⁿ × [-T, 0].

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