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Diffusion-dominated asymptotics of solution to chemotaxis model. (English) Zbl 1255.35050
Summary: The paper contains results on the asymptotic behavior, as \(t \rightarrow +\infty \), of small solutions to simplified Keller-Segel problem modeling chemotaxis in the whole space \({\mathbb R^2}\). We prove that the multiple of the heat kernel is a surprisingly good approximation of solutions.

MSC:
35B40 Asymptotic behavior of solutions to PDEs
35K57 Reaction-diffusion equations
92C17 Cell movement (chemotaxis, etc.)
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