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math.AP2022
Liouville-type theorems for the Lane-Emden equation in the half-space and cones
Louis Dupaigne, Alberto Farina, Troy Petitt
We prove that 0 the only classical solution of the Lane-Emden equation in the half-space which is stable outside a compact set. We also consider weak solutions and the case of gene…
math.AP2022
Sharp well-posedness and blowup results for parabolic systems of the Keller-Segel type
Piotr Biler, Alexandre Boritchev, Lorenzo Brandolese
We study two toy models obtained after a slight modification of the nonlinearity of the usual doubly parabolic Keller-Segel system. For these toy models, both consisting of a syste…