The singular limits of Riemann solutions to a chemotaxis model with flux perturbation. (English) Zbl 1538.35215
Summary: The phenomenon of chemotactic collapse is identified and analyzed for a chemotaxis model in a conservative form when the diffusion effect is neglected by using a singular perturbation of flux function. It is proven rigorously that the Riemann solutions for the scaled chemotaxis system converge to the corresponding ones for a non-strictly hyperbolic system of conservation laws when the scaled parameter tends to zero. In addition, in some particular situations, the delta standing wave is obtained in the limit situation, which can be used to explain reasonably the phenomenon of chemotactic collapse.
© 2019 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
© 2019 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
MSC:
| 35L65 | Hyperbolic conservation laws |
| 35L67 | Shocks and singularities for hyperbolic equations |
| 35B25 | Singular perturbations in context of PDEs |
| 90B20 | Traffic problems in operations research |
| 92C17 | Cell movement (chemotaxis, etc.) |
Keywords:
chemotaxis model; delta standing wave; hyperbolic conservation law; Riemann problem; singular perturbationReferences:
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