Volume 3, Issue 1
The Relaxation Limit of a Quasi-Linear Hyperbolic-Parabolic Chemotaxis System Modeling Vasculogenesis

Qingqing Liu, Hongyun Peng & Zhi-An Wang

Commun. Math. Anal. Appl., 3 (2024), pp. 1-18.

Published online: 2024-03

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  • Abstract

This paper is concerned with the relaxation limit of a three-dimensional quasi-linear hyperbolic-parabolic chemotaxis system modeling vasculogenesis when the initial data are prescribed around a constant ground state. When the relaxation time tends to zero (i.e. the damping is strong), we show that the strong-weak limit of the cell density and chemoattractant concentration satisfies a parabolic-elliptic Keller-Segel type chemotaxis system in the sense of distribution.

  • AMS Subject Headings

35L60, 35L04, 35B40, 35Q92

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COPYRIGHT: © Global Science Press

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@Article{CMAA-3-1, author = {Liu , QingqingPeng , Hongyun and Wang , Zhi-An}, title = {The Relaxation Limit of a Quasi-Linear Hyperbolic-Parabolic Chemotaxis System Modeling Vasculogenesis}, journal = {Communications in Mathematical Analysis and Applications}, year = {2024}, volume = {3}, number = {1}, pages = {1--18}, abstract = {

This paper is concerned with the relaxation limit of a three-dimensional quasi-linear hyperbolic-parabolic chemotaxis system modeling vasculogenesis when the initial data are prescribed around a constant ground state. When the relaxation time tends to zero (i.e. the damping is strong), we show that the strong-weak limit of the cell density and chemoattractant concentration satisfies a parabolic-elliptic Keller-Segel type chemotaxis system in the sense of distribution.

}, issn = {2790-1939}, doi = {https://doi.org/10.4208/cmaa.2024-0001}, url = {http://global-sci.org/intro/article_detail/cmaa/22938.html} }
TY - JOUR T1 - The Relaxation Limit of a Quasi-Linear Hyperbolic-Parabolic Chemotaxis System Modeling Vasculogenesis AU - Liu , Qingqing AU - Peng , Hongyun AU - Wang , Zhi-An JO - Communications in Mathematical Analysis and Applications VL - 1 SP - 1 EP - 18 PY - 2024 DA - 2024/03 SN - 3 DO - http://doi.org/10.4208/cmaa.2024-0001 UR - https://global-sci.org/intro/article_detail/cmaa/22938.html KW - Hyperbolic-parabolic model, vasculogenesis, diffusion, relaxation limit. AB -

This paper is concerned with the relaxation limit of a three-dimensional quasi-linear hyperbolic-parabolic chemotaxis system modeling vasculogenesis when the initial data are prescribed around a constant ground state. When the relaxation time tends to zero (i.e. the damping is strong), we show that the strong-weak limit of the cell density and chemoattractant concentration satisfies a parabolic-elliptic Keller-Segel type chemotaxis system in the sense of distribution.

Liu , QingqingPeng , Hongyun and Wang , Zhi-An. (2024). The Relaxation Limit of a Quasi-Linear Hyperbolic-Parabolic Chemotaxis System Modeling Vasculogenesis. Communications in Mathematical Analysis and Applications. 3 (1). 1-18. doi:10.4208/cmaa.2024-0001
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