Electronic Journal of Differential Equations,
Vol. 2008(2008), No. 30, pp. 1-18.
Title: Degenerate stationary problems with homogeneous
boundary conditions
Authors: Kaouther Ammar (TU Berlin, Institut fur Mathematik, Germany)
Hicham Redwane (Univ. Hassan 1, Settat, Morocco)
Abstract:
We are interested in the degenerate problem
$$
b(v)-\hbox{ div}a(v,\nabla g(v))=f
$$
with the homogeneous boundary condition
$g(v)=0$ on some part of the boundary.
The vector field $a$ is supposed to satisfy the
Leray-Lions conditions and the functions $b,g$ to be continuous,
nondecreasing and to verify the normalization condition
$b(0)=g(0)=0$ and the range condition $R(b+g)=\mathbb{R}$.
Using monotonicity methods, we prove existence and
comparison results for renormalized entropy solutions in
the $L^1$ setting.
Submitted January 8, 2008. Published February 28, 2008.
Math Subject Classifications: 35K65, 35F30, 35K35, 65M12.
Key Words: Degenerate; homogenous boundary conditions; diffusion;
continuous flux.