Unbounded mass radial solutions for the Keller-Segel equation in the disk

Jean-Baptiste Casteras 1, 2 Denis Bonheure 1, 2 Carlos Román 3
1 MEPHYSTO - Quantitative methods for stochastic models in physics
LPP - Laboratoire Paul Painlevé - UMR 8524, ULB - Université Libre de Bruxelles [Bruxelles], Inria Lille - Nord Europe
Abstract : We construct several families of radial solutions for the stationary Keller-Segel equation in the disk. The first family consists in solutions which blow up at the origin, as a parameter goes to zero, and concentrate on the boundary. The second is made of solutions which blow up at the origin and concentrate on an interior sphere, while the solutions of the third family blow up at the origin and concentrate simultaneously on an interior sphere and on the boundary. Finally, we also show how to construct more families of multi-layered radial solutions provided a suitable non degeneracy assumption is satisfied.
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https://hal.archives-ouvertes.fr/hal-01665514
Contributor : Jean-Baptiste Casteras <>
Submitted on : Saturday, December 16, 2017 - 7:37:49 AM
Last modification on : Sunday, March 31, 2019 - 1:29:37 AM

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  • HAL Id : hal-01665514, version 1
  • ARXIV : 1709.10471

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Jean-Baptiste Casteras, Denis Bonheure, Carlos Román. Unbounded mass radial solutions for the Keller-Segel equation in the disk. 2017. ⟨hal-01665514⟩

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