WIAS Preprint No. 938, (2004)

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.

Appeared in

  • Nonlinear elliptic and parabolic problems, 151--188, Prog. Nonlinear Differential Equations Appl., 64, Birkhäuser, Basel, 2005

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