The nonsymmetric case of the Keller-Segel model in chemotaxis: some recent results.
This paper studies the non-symmetric (e.g. non-radical) case of the Keller-Segel, reaction-diffuson model of chemotaxis. It reviews known global existence and blow-up results. Particular emphasis is placed on ``non-symmetric'' solutions, and it is proved that if a solution blows-up in finite time then blow up takes place at the boundary of a smooth domain. Nontrivial stationary solutions are established using variational methods. The paper complements that of \textit{M. A. Herrero} [Asymptotic properties of reaction-diffusion systems modeling chemotaxis. In: Spigler, Renato (ed.) Applied and industrial mathematics, Venice-2, 1998. Dordrecht, Kluwer, 89--108 (2000; Zbl 1006.35052)].
scientific article; zbMATH DE number 1722188