Diffusion equation with anisotropic coefficients arise in many environmental topics, heat transfer, groundwater flow and transport problems, petroleum reservoir simulations, hydrodynamic simulations, ... These problems are characterized by a full rank diffusion tensor, that is diagonal only if the reference system is aligned with the principal direction of anisotropy (Bear). Numerical difficult...

, A numerical solution to the integro-differential equation describing the energy'distribution of a beam of electrons which has passed through matter, losing energy by radiation only, has been obtained utilizing a finite difference mesh method. Solutions were obtained for thicknesses of up to 0.1 radiation lengths for a complete screening approximation to the energy loss equation. The accuracy ...

In this paper, the authors consider the first boundary value problem for the nonlinear reaction diffusion equation: ut −∆um = αup1 in Ω, a smooth bounded domain in Rd(d ≥ 1) with the zero lateral boundary condition and with a positive initial condition, m ∈ ]0, 1[ (fast diffusion problem), α ≥ 0 and p1 ≥ m. Sufficient conditions on the initial data are obtained for the solution to vanish or bec...