Density Dependent Diffusion Equation in Population Dynamics: Stabilization to Equilibrium

摘要

A problem (P) of the theory of population dynamics over a finite habitat composed by two different age groups when the boundary conditions are supposed that no individuals can leave or enter the habitat, is considered. This problem is studied as a nonlinear evolution problem. The large time behavior of the solutions of P is discussed and the results of existence, uniqueness, and regularity of solutions of P are reported. The construction of a Lyapunov functional for the contraction property for solutions of P and for the relations between P and the Dirichlet problem is discussed.