Global existence of solutions to a hyperbolic-parabolic system

Zhang, Mei; Zhu, Changjiang

doi:10.1090/S0002-9939-06-08773-9

Global existence of solutions to a hyperbolic-parabolic system
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by Mei Zhang and Changjiang Zhu PDF

Proc. Amer. Math. Soc. 135 (2007), 1017-1027 Request permission

Abstract:

In this paper, we investigate the global existence of solutions to a hyperbolic-parabolic model of chemotaxis arising in the theory of reinforced random walks. To get $L^2$-estimates of solutions, we construct a nonnegative convex entropy of the corresponding hyperbolic system. The higher energy estimates are obtained by the energy method and a priori assumptions.

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