%0 Journal Article
%T Parabolic systems with coupled boundary conditions
%A Stefano Cardanobile
%A Delio Mugnolo
%J Mathematics
%D 2008
%I arXiv
%X We consider elliptic operators with operator-valued coefficients and discuss the associated parabolic problems. The unknowns are functions with values in a Hilbert space $W$. The system is equipped with a general class of coupled boundary conditions of the form $f_{|\partial\Omega}\in \mathcal Y$ and $\frac{\partial f}{\partial \nu}\in {\mathcal Y}^\perp$, where $\mathcal Y$ is a closed subspace of $L^2(\partial\Omega;W)$. We discuss well-posedness and further qualitative properties, systematically reducing features of the parabolic system to operator-theoretical properties of the orthogonal projection onto $\mathcal Y$.
%U http://arxiv.org/abs/0812.3813v2