Modeling of drift-diffusion systems
- Stephan, Holger
2010 Mathematics Subject Classification
- 35K55 80A20 82D37 82C31 35B50 35G25
- drift-diffusion systems, energy models, free energy, Lyapunov functions, positive solutions, inverse Hessian, cross diffusion
We derive drift-diffusion systems describing transport processes starting from free energy and equilibrium solutions by a unique method. We include several statistics, heterostructures and cross diffusion. The resulting systems of nonlinear partial differential equations conserve mass and positivity, and have a Lyapunov function (free energy). Using the inverse Hessian as mobility, non-degenerate diffusivity matrices turn out to be diagonal, or - in the case of cross diffusion - even constant.
- Zeitschrift fuer Angewandte Mathematik und Physik (ZAMP) 60 (2009) pp.33-53