Anisotropic parabolic-elliptic systems with degenerate thermal conductivity.

In this paper, we investigate the existence and regularity of a capacity solution for a coupled nonlinear anisotropic parabolic-elliptic system, where the elliptic component of the parabolic equation involves thermal conductivities $ a_{i}(u) $ a i (u) that satisfy $ \lim _{s\rightarrow +\infty }a_{i}(s)=0 $ lim s → + ∞ a i (s) = 0 for all $ i=1,\ldots,N $ i = 1 , ... , N. We work with anisotropic Sobolev spaces and use Schauder's fixed-point theorem to find weak solutions to approximate problems. In addition, we validate the convergence of a subsequence of approximate solutions to a capacity solution. [ABSTRACT FROM AUTHOR]