Global well-posedness and large-time behavior of a hyperbolic-parabolic model in an exterior domain

Abstract

<p style='text-indent:20px;'>We consider a hyperbolic-parabolic system derived from a limiting case of chemotaxis model in an exterior domain. By energy method we prove global existence for the initial-boundary value problem in an exterior domain when the initial data is a small perturbation around constant equilibrium states, and the solutions converge to the states at an algebraic decay rate as time goes to infinity.</p>