Global Existence and Asymptotic Behavior of Solutions to a Semilinear Hyperbolic Model of Chemotaxis

Details Global Existence and Asymptotic Behavior of Solutions to a Semilinear Hyperbolic Model of Chemotaxis Global Existence and Asymptotic Behavior of Solutions to a Semilinear Hyperbolic Model of Chemotaxis

2012-03-24

arxiv.org/abs/1203.5404v2

Mathematics

Analysis of PDEs

Scientific paper

We consider a general hyperbolic model of chemotaxis in the multidimensional case. For this system we show the global existence of smooth solutions to the Cauchy problem and we determine their asymptotic behavior. Since this model does not enter in the classical framework of dissipative problems, we analyze it combining the features of the hyperbolic and the parabolic parts and using detailed decay estimates of the Green function.

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