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Asymptotic stability of exogenous chemotaxis systems with physical boundary conditions. (English) Zbl 1476.35288

The chemotaxis-consumption system \[u_t=u_{xx}-(uv_x)_x,\] \[v_t=Dv_{xx}-uv,\] on the interval \(x\in(0,1)\) is studied with the no-flux boundary conditions. The main result is that the nonconstant steady state is locally asymptotically stable as it has been shown also for slightly different aerotaxis equations in [P. Knosalla and T. Nadzieja, Appl. Math. 42, No. 2–3, 125–135 (2015; Zbl 1331.92060)].

MSC:

35Q92 PDEs in connection with biology, chemistry and other natural sciences
35K51 Initial-boundary value problems for second-order parabolic systems
35B40 Asymptotic behavior of solutions to PDEs
92C17 Cell movement (chemotaxis, etc.)

Citations:

Zbl 1331.92060
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References:

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