Uniqueness for inhomogeneous Dirichlet problem for elliptic–parabolic equations

@inproceedings{Andreianov2007UniquenessFI,
  title={Uniqueness for inhomogeneous Dirichlet problem for elliptic–parabolic equations},
  author={Boris Andreianov and Noureddine Igbida},
  year={2007}
}
We show the L^1 contraction and comparison principle for weak (and, more generally, renormalized) solutions of the elliptic-parabolic problem j(v)_t−div(∇w+ F(w)) = f(t, x), w = \phi(v) in (0, T)×\Omega ⊂ IR+×IR^N with inhomogeneous Dirichlet boundary datum g ∈ L^2(0,T;W^{1,2}(\Omega)) for w (which is taken in the sense w − g ∈ L^2(0, T;H^1_0 (\Omega))) and initial datum j_o ∈ L^1(\Omega) for j(v). Here \phi, j are nondecreasing, and we assume F just continuous. Our proof consists in doubling… CONTINUE READING