Existence of Nonnegative Solutions for a Fractional Parabolic Equation in the Entire Space

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We study the existence of nonnegative solutions of a parabolic problem \( \frac{\partial u}{\partial t}=-{\left(-\Delta \right)}^{\frac{\alpha }{2}}u+\frac{c}{{\left|x\right|}^{\alpha }}u \) in d × (0, T). Here, 0 < α < min(2, d), \( {\left(-\Delta \right)}^{\frac{\alpha }{2}} \) is the fractional Laplacian on d and u0 ∈ L2(d).

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Correspondence to T. Kenzizi.

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Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 71, No. 8, pp. 1064–1072, August, 2019.

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Kenzizi, T. Existence of Nonnegative Solutions for a Fractional Parabolic Equation in the Entire Space. Ukr Math J 71, 1214–1223 (2020) doi:10.1007/s11253-019-01708-6

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