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Global generalized solutions to a parabolic-elliptic Keller-Segel system with singular sensitivity. (English) Zbl 1439.35486

The author introduces a new concept of generalized solutions to the parabolic-elliptic Keller-Segel model of chemotaxis with the sensitivity function \(\chi\frac{1}{v}\) considered in a bounded smooth domain of \({\mathbb R}^n\) and supplemented with the homogeneous Neumann boundary conditions. Then, the results on the global existence of solutions are improved up to the condition \(\chi<\frac{n}{n-2}\) guaranteeing that property.

MSC:

35Q92 PDEs in connection with biology, chemistry and other natural sciences
35D99 Generalized solutions to partial differential equations
35K55 Nonlinear parabolic equations
92C17 Cell movement (chemotaxis, etc.)
35A01 Existence problems for PDEs: global existence, local existence, non-existence
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References:

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