WIAS Preprint No. 1120, (2006)

Modeling of drift-diffusion systems



Authors

  • Stephan, Holger

2010 Mathematics Subject Classification

  • 35K55 80A20 82D37 82C31 35B50 35G25

Keywords

  • drift-diffusion systems, energy models, free energy, Lyapunov functions, positive solutions, inverse Hessian, cross diffusion

Abstract

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.

Appeared in

  • Zeitschrift fuer Angewandte Mathematik und Physik (ZAMP) 60 (2009) pp.33-53

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