On the uniqueness of solutions for nonlinear elliptic-parabolic equations
- Gajewski, Herbert
- Skrypnik, Igor V.
2010 Mathematics Subject Classification
- 35B45 35K15 35K20 35K65
- Nonlinear parabolic equations, bounded solutions, uniqueness, nonstandard assumptions, degenerate type
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.
- J. Evol. Equ., 3 (2003), pp. 247-281