Journal article
ON A HYPERBOLIC-PARABOLIC SYSTEM MODELING CHEMOTAXIS
Mathematical models & methods in applied sciences, Vol.21(8), pp.1631-1650
08/01/2011
DOI: 10.1142/S0218202511005519
Abstract
We investigate local/global existence, blowup criterion and long-time behavior of classical solutions for a hyperbolic-parabolic system derived from the Keller-Segel model describing chemotaxis. It is shown that local smooth solution blows up if and only if the accumulation of the L-infinity norm of the solution reaches infinity within the lifespan. Our blowup criteria are consistent with the chemotaxis phenomenon that the movement of cells (bacteria) is driven by the gradient of the chemical concentration.
Furthermore, we study the long-time dynamics when the initial data is sufficiently close to a constant positive steady state. By using a new Fourier method adapted to the linear flow, it is shown that the smooth solution exists for all time and converges exponentially to the constant steady state with a frequency-dependent decay rate as time goes to infinity.
Details
- Title: Subtitle
- ON A HYPERBOLIC-PARABOLIC SYSTEM MODELING CHEMOTAXIS
- Creators
- Dong Li - University of IowaTong Li - University of IowaKun Zhao - The Ohio State University
- Resource Type
- Journal article
- Publication Details
- Mathematical models & methods in applied sciences, Vol.21(8), pp.1631-1650
- Publisher
- WORLD SCIENTIFIC PUBL CO PTE LTD
- DOI
- 10.1142/S0218202511005519
- ISSN
- 0218-2025
- eISSN
- 1793-6314
- Number of pages
- 20
- Grant note
- Mathematics Department of University of Iowa University of Iowa 0908032; DMS 0807406; 0635561 / National Science Foundation
- Language
- English
- Date published
- 08/01/2011
- Academic Unit
- Mathematics
- Record Identifier
- 9984241042702771
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