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Asymptotic stability of a composite wave of two traveling waves to a hyperbolic-parabolic system modeling chemotaxis. (English) Zbl 1273.35278

Summary: We study the asymptotic stability of a composite wave consisting of two traveling waves to a hyperbolic-parabolic system modeling repulsive chemotaxis. On the basis of elementary energy estimates, we show that the composite wave is asymptotically stable under general initial perturbations, which are not necessarily zero integral. As an application, we obtain a similar result for this system in the presence of a boundary.

MSC:

35Q92 PDEs in connection with biology, chemistry and other natural sciences
35M30 Mixed-type systems of PDEs
35B35 Stability in context of PDEs
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