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- W3157707811 abstract "The Cauchy problem for the Hardy–Hénon parabolic equation is studied in the critical and subcritical weighted Lebesgue spaces on the Euclidean space R d . In earlier works, the well-posedness of singular initial data and the existence of non-radial forward self-similar solutions to the problem were shown for the Hardy and Fujita cases ( γ ≤ 0 ). The weighted spaces are used to treat the potential | x | γ as an increase or decrease in the weight, which enables us to prove the well-posedness of the problem for all γ , with − min { 2 , d } < γ , including the Hénon case ( γ > 0 ). As a by-product of global existence, self-similar solutions to the problem are established for all γ without restrictions. Furthermore, the non-existence of a local solution for supercritical data is also shown. Therefore, our critical exponent, s c is optimal with regard to solvability." @default.
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- W3157707811 date "2022-09-01" @default.
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- W3157707811 title "Optimal well-posedness and forward self-similar solution for the Hardy–Hénon parabolic equation in critical weighted Lebesgue spaces" @default.
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- W3157707811 doi "https://doi.org/10.1016/j.na.2022.112931" @default.
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