Abstract
In this paper we are concerned with the study of the existence of solutions of a nonlinear parabolic system with density-dependent diffusion, subject to homogeneous third-type boundary conditions. A comparison result is shown that allows the study of the asymptotic behavior of the solutions via the same methods used for systems with classical diffusion. Finally an application of the results to an epidemic system is presented. Sufficient conditions are given for the positivity of the solution of this system.
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