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

摘要

We consider a general hyperbolic-parabolic 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 by combining the features of the hyperbolic and the parabolic parts and by using detailed decay estimates of the Green function.