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- ItemModeling of drift-diffusion systems(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2006) Stephan, HolgerWe 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