1. Contraction for large perturbations of traveling waves in a hyperbolic–parabolic system arising from a chemotaxis model
- Author
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Moon-Jin Kang, Kyudong Choi, Alexis F. Vasseur, and Young-Sam Kwon
- Subjects
Physics ,Tumor angiogenesis ,Applied Mathematics ,Mathematical analysis ,Chemotaxis ,Stability (probability) ,Quantitative Biology::Cell Behavior ,Parabolic system ,Mathematics - Analysis of PDEs ,Modeling and Simulation ,FOS: Mathematics ,Traveling wave ,Sensitivity (control systems) ,Contraction (operator theory) ,Analysis of PDEs (math.AP) - Abstract
We consider a hyperbolic–parabolic system arising from a chemotaxis model in tumor angiogenesis, which is described by a Keller–Segel equation with singular sensitivity. It is known to allow viscous shocks (so-called traveling waves). We introduce a relative entropy of the system, which can capture how close a solution at a given time is to a given shock wave in almost [Formula: see text]-sense. When the shock strength is small enough, we show the functional is non-increasing in time for any large initial perturbation. The contraction property holds independently of the strength of the diffusion.
- Published
- 2020
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