Continuation of the solution to the Chemotaxis Problem Beyond its Blow-up

Mario Primicerio, Boris Zaltzman

Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review

Abstract

In this paper we deal with classical solutions to the chemotaxis problem and characterize cases of blow-up. Next, we define continuation of the classical solutions beyond blow-up time To. This definition is in fact nontrivial because, although allowing finite mass to concentrate in the origin after To (without prescribing its amount as a function of time), it identifies the solution uniquely. Moreover, two ways of regularizing the problem are provided: they look quite natural and they are shown to converge to the solution.
Original languageEnglish
Title of host publication Free Boundary Problems
Subtitle of host publicationTheory and Applications
EditorsAugusto Visintin, Claudio Verdi, Pierluigi Colli
PublisherBirkhauser Verlag Basel
Pages255-264
Volume147
StatePublished - 2003

Publication series

NameInternational Series of Numerical Mathematics
Volume147

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