Abstract
We study the existence and the longterm behavior of solutions of a parabolic equation governed by the p-Laplacian with nonlinear growth terms that are coupled with the solutions of a system of ordinary differential equations. The existence and the uniqueness are shown by using a fixed point argument and the longterm behavior of solutions is discussed by using energy estimates together with the nonlinear peculiarity of the p-Laplacian. Numerical simulations are carried out by using a Finite Volume Method for spatial treatment. For time integration of the p-Laplacian, an implicit Euler method is used, and direct integration for the ODE system.
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