Entropy-dissipative discretization of nonlinear diffusion equations and discrete Beckner inequalities (Q2798135)

The paper is concerned with the time decay of fully discrete finite volume solutions to the nonlinear diffusion equation with Neumann boundary conditions. The paper also gives estimates on the decay rates from the entropy decay estimates in a continuous case. The finite volume scheme for the nonlinear diffusion equation is presented followed by the generalized Beckner's inequalities at the continuous and the discrete level. Some numerical examples are presented in one and two space dimensions. Several theorems are stated and proved. The paper may provide new directions to the solution of the diffusion problems in plasma Physics and semiconductor theory.