WIAS Preprint No. 754, (2002)

On the uniqueness of solutions for nonlinear elliptic-parabolic equations



Authors

  • Gajewski, Herbert
  • Skrypnik, Igor V.

2010 Mathematics Subject Classification

  • 35B45 35K15 35K20 35K65

Keywords

  • Nonlinear parabolic equations, bounded solutions, uniqueness, nonstandard assumptions, degenerate type

Abstract

We prove existence, boundedness and uniqueness of solutions to Cauchy-Dirichlet problems for elliptic-parabolic systems, where the specific coupling is such that the solution of the elliptic equation forms a drift term in the parabolic equation. Such systems arise as mathematical models of various applied problems, for instance, drift-diffusion processes in semiconductors and segregation processes in alloys. Our basic assumptions are thermodynamically motivated.

Appeared in

  • J. Evol. Equ., 3 (2003), pp. 247-281

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