Journal
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
Volume 45, Issue 11, Pages 6739-6765Publisher
WILEY
DOI: 10.1002/mma.8204
Keywords
asymptotic behavior; chemotaxis; hyperbolic-parabolic; network; transmission condition
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Funding
- NSFC [11771062, 11971082]
- Natural Science Foundation of Chongqing [cstc2021jcyj-msxmX1051]
- Fundamental Research Funds for the Central Universities [2020CDJQYZ001, 2019CDJCYJ001, 2021CDJQY-009]
- Chongqing Key Laboratory of Analytic Mathematics and Applications
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In this paper, we discuss a hyperbolic-parabolic system on a network. The global existence of solution to this problem with suitable the transmission conditions at interior is obtained by energy estimates. Moreover, for the case of acyclic network, we prove the existence and uniqueness of stationary solution to the system and show that the stationary solution provides asymptotic profiles for a class of global solutions.
In this paper, we discuss a hyperbolic-parabolic system on a network. The global existence of solution to this problem with suitable the transmission conditions at interior is obtained by energy estimates. Moreover, for the case of acyclic network, we prove the existence and uniqueness of stationary solution to the system and show that the stationary solution provides asymptotic profiles for a class of global solutions.
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