Unbounded mass radial solutions for the ...
Document type :
Pré-publication ou Document de travail
Title :
Unbounded mass radial solutions for the Keller-Segel equation in the disk
Author(s) :
Casteras, Jean-Baptiste [Auteur]
Quantitative methods for stochastic models in physics [MEPHYSTO]
Département de mathématiques Université Libre de Bruxelles
Bonheure, Denis [Auteur]
Quantitative methods for stochastic models in physics [MEPHYSTO]
Département de mathématiques Université Libre de Bruxelles
Román, Carlos [Auteur]
Laboratoire Jacques-Louis Lions [LJLL]
Quantitative methods for stochastic models in physics [MEPHYSTO]
Département de mathématiques Université Libre de Bruxelles
Bonheure, Denis [Auteur]
Quantitative methods for stochastic models in physics [MEPHYSTO]
Département de mathématiques Université Libre de Bruxelles
Román, Carlos [Auteur]
Laboratoire Jacques-Louis Lions [LJLL]
HAL domain(s) :
Mathématiques [math]/Equations aux dérivées partielles [math.AP]
English abstract : [en]
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 ...
Show more >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.Show less >
Show more >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.Show less >
Language :
Anglais
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