On the Asymptotic Behavior of the Solutions of a Class of Anisotropic Initial-Boundary Value Problems

In this paper, we investigate a class of anisotropic initial-boundary value problems, involving the Finsler-Laplacian. Firstly, by using a first-order differential inequality technique, we provide some appropriate conditions on the data which guarantee the blow-up of the solution at some explicit finite time. Next, under different appropriate conditions on the data, we will make use of a comparison principle to prove the global boundedness of the solution. Finally, by using a maximum principle for an appropriate P-function, in the sense of L.E. Payne, we derive some explicit exponential time decay bounds for the solution and its derivatives..