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Measure valued solutions of the 2D Keller-Segel system. (English) Zbl 1256.35180

Summary: We develop a theory of global measure-valued solutions for the classical Keller-Segel model. These solutions are obtained considering the limit of solutions of a regularized problem. We also prove that different regularizations yield different limit measures in the case in which classical solutions of the Keller-Segel system are not globally defined in time.

MSC:

35Q92 PDEs in connection with biology, chemistry and other natural sciences
35R06 PDEs with measure
35B27 Homogenization in context of PDEs; PDEs in media with periodic structure
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