Large time behavior of solution to an attraction-repulsion chemotaxis system with logistic source in three dimensions. (English) Zbl 1366.35071
The authors consider the non-homogeneous quasilinear diffusion-transport problem in a convex bounded smooth domain in \(\mathbb R^3\). Boundary conditions are Neumann homogeneous. The source function \(f(u)=u(1-\mu u^\gamma)\), \(\gamma\geq1\), \(\mu>0\), depends on one unknown function. Global existence and asymptotic stability of a unique bounded solution are proven under assumption that initial distributions are from \(W^{1,\infty}\) and some inequalities for parameters hold. Also, convergence of the solution to the steady state in \(L^\infty\) is shown.
Reviewer: Ilya A. Chernov (Petrozavodsk)
MSC:
| 35K51 | Initial-boundary value problems for second-order parabolic systems |
| 35A02 | Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness |
| 35B40 | Asymptotic behavior of solutions to PDEs |
| 35A01 | Existence problems for PDEs: global existence, local existence, non-existence |
Keywords:
chemotaxis; attraction-repulsion; global existence; uniqueness; boundedness; logistic source; asymptotic behaviourReferences:
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