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The singular limits of Riemann solutions to a chemotaxis model with flux perturbation
Author(s) -
Shen Chun,
Sun Meina
Publication year - 2019
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.201800046
Subject(s) - chemotaxis , perturbation (astronomy) , riemann hypothesis , mathematical analysis , singular perturbation , riemann problem , mathematics , limit (mathematics) , conservation law , flux (metallurgy) , physics , quantum mechanics , chemistry , biochemistry , receptor , organic chemistry
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.