Eventual smoothness and asymptotic behaviour of solutions to a chemotaxis system perturbed by a logistic growth. (English) Zbl 1409.35046
The parabolic chemotaxis system with logistic-type source and homogeneous Neumann conditions is studied in convex domains of \({\mathbb R}^n\), \(n\geq 1\). The existence of very weak global in time solutions is shown, as well as the boundedness and regularity (for large time) of solutions are studied. Illustrations of dynamics of the system are given for \(n\leq 3\) by means of numerical simulations.
Reviewer: Piotr Biler (Wrocław)
MSC:
| 35B65 | Smoothness and regularity of solutions to PDEs |
| 35B40 | Asymptotic behavior of solutions to PDEs |
| 92C17 | Cell movement (chemotaxis, etc.) |
| 35K51 | Initial-boundary value problems for second-order parabolic systems |
| 35K59 | Quasilinear parabolic equations |
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