Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Parabolic systems with coupled boundary conditions   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 $\mathcal Y$.

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The categories of this paper are: astro-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: supr-con
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The categories of this paper are: hep-ph
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The categories of this paper are: econ
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The categories of this paper are: ao-sci
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The categories of this paper are: adap-org
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The categories of this paper are: quant-ph
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The categories of this paper are: eess
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The categories of this paper are: cmp-lg
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The categories of this paper are: cs
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The categories of this paper are: chao-dyn
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The categories of this paper are: cond-mat
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The categories of this paper are: gr-qc
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The categories of this paper are: dg-ga
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The categories of this paper are: atom-ph