✦ LIBER ✦
The steady states and convergence to equilibria for a 1-D chemotaxis model with volume-filling effect
✍ Scribed by Yanyan Zhang
- Publisher
- John Wiley and Sons
- Year
- 2009
- Tongue
- English
- Weight
- 409 KB
- Volume
- 33
- Category
- Article
- ISSN
- 0170-4214
- DOI
- 10.1002/mma.1147
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✦ Synopsis
Communicated by R. Racke
We consider a chemotaxis model with volume-filling effect introduced by Hillen and Painter. They also proved the existence of global solutions for a compact Riemannian manifold without boundary. Moreover, the existence of a global attractor in W 1,p (X ⊂ R n ), p>n, p 2, was proved by Wrzosek. He also proved that the x-limit set consists of regular stationary solutions. In this paper, we prove that the 1-D stationary problem has at most an infinitely countable number of regular solutions. Furthermore, we show that as t →∞ the solution of the 1-D evolution problem converges to an equilibrium in W 1,p , p 2.