Existence and uniqueness results for reaction-diffusion processes of electrically charged species
- Gajewski, Herbert
- Skrypnik, Igor V.
2010 Mathematics Subject Classification
- 35B45 35K15 35K20 35K65
- Nonlinear elliptic-parabolic systems, nonlocal drift, global bounded solutions, uniqueness, nonstandard assumptions, degenerate typ
We study initial-- boundary value problems for elliptic--parabolic systems of nonlinear partial differential equations describing drift--diffusion processes of electrically charged species in N--dimensional bounded Lipschitzian domains. We include Fermi--Dirac statistics and admit nonsmooth material coefficients. We prove existence and uniqueness of bounded global solutions.
- Nonlinear elliptic and parabolic problems, 151--188, Prog. Nonlinear Differential Equations Appl., 64, Birkhäuser, Basel, 2005