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Contraction for large perturbations of traveling waves in a hyperbolic-parabolic system arising from a chemotaxis model
| Content Provider | Semantic Scholar |
|---|---|
| Author | Choi, Kyudong Kang, Moon-Jin Kwon, Young-Sam Vasseur, Alexis |
| Copyright Year | 2019 |
| Abstract | We consider a hyperbolic-parabolic system arising from a chemotaxis model in 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 $L^2$-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. |
| File Format | PDF HTM / HTML |
| DOI | 10.1142/s0218202520500104 |
| Alternate Webpage(s) | https://arxiv.org/pdf/1904.12169v1.pdf |
| Alternate Webpage(s) | https://web.ma.utexas.edu/users/vasseur/documents/preprints/Kyudong.pdf |
| Alternate Webpage(s) | http://arxiv-export-lb.library.cornell.edu/pdf/1904.12169 |
| Alternate Webpage(s) | https://doi.org/10.1142/s0218202520500104 |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
