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Exclusion of boundary blowup for 2D chemotaxis system provided with Dirichlet boundary condition for the Poisson part. (English) Zbl 1285.35121

Summary: We study a chemotaxis system on bounded domain in two dimensions where the formation of chemical potential is subject to the Dirichlet boundary condition. For such a system the solution is kept bounded near the boundary and hence the blowup set is composed of a finite number of interior points. If the initial total mass is \(8\pi\) and the domain is close to a disc then the solution exhibits a collapse in infinite time of which movement is subject to a gradient flow associated with the Robin function.

MSC:

35Q92 PDEs in connection with biology, chemistry and other natural sciences
92C17 Cell movement (chemotaxis, etc.)
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