Global Existence and Extinction of Weak Solutions to a Class of Semiconductor Equations with Fast Diffusion Terms.

The article presents research on the global existence and extinction of weak solutions to a class of semiconductor equations with fast diffusion terms. It shows the existence result for general nonlinear diffusivities for the Dirichlet-Neumann mixed boundary value problem. It investigates the extinction phenomenon of weak solutions for homogeneous Dirichlet boundary problem. The p-Laplacian (Lp)-integral model estimate method a crucial lemma on differential inequality were employed to prove the result of sufficient conditions on the extinction and decay estimates of solutions. It notes that the technique has been successfully applied to the porous medium equation.