Global properties of pair diffusion models (Q2747828)

The authors investigate global properties of pair diffusion models with non-smooth data arising in semiconductor technology. The corresponding model equations are nonlinear parabolic PDEs for the mobile species and ODEs involving reaction terms for immobile species. They are coupled with a nonlinear Poisson equation for the chemical potential of the electrons. From assumptions more general than homogeneity of the materials, authors proof a energy estimate with methods of convex analysis. Thereafter, global upper and lower bounds in the \(L^ {\infty}\) norm for solutions of the initial boundary value problem are obtained. Finally, the study of the asymptotic behaviour of solutions is treated.