Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Homogenization of the first initial boundary-value problem for parabolic
  systems: operator error estimates   Let $\mathcal{O}\subset\mathbb{R}^d$ be a bounded domain of class $C^{1,1}$.
In $L_2(\mathcal{O};\mathbb{C}^n)$, we consider a selfadjoint matrix second
order elliptic differential operator $B_{D,\varepsilon}$,
$0<\varepsilon\leqslant1$, with the Dirichlet boundary condition. The principal
part of the operator is given in a factorized form. The operator involves first
and zero order terms. The operator $B_{D,\varepsilon}$ is positive definite;
its coefficients are periodic and depend on $\mathbf{x}/\varepsilon$. We study
the behavior of the operator exponential $e^{-B_{D,\varepsilon}t}$, $t>0$, as
$\varepsilon\rightarrow 0$. We obtain approximations for the exponential
$e^{-B_{D,\varepsilon}t}$ in the operator norm on
$L_2(\mathcal{O};\mathbb{C}^n)$ and in the norm of operators acting from
$L_2(\mathcal{O};\mathbb{C}^n)$ to the Sobolev space
$H^1(\mathcal{O};\mathbb{C}^n)$. The results are applied to homogenization of
solutions of the first initial boundary-value problem for parabolic systems.

8
The categories of this paper are: hep-ex
13
The categories of this paper are: quant-ph
32
The categories of this paper are: atom-ph
27
The categories of this paper are: comp-gas
1
The categories of this paper are: cs
25
The categories of this paper are: patt-sol
4
The categories of this paper are: cond-mat
20
The categories of this paper are: acc-phys
37
The categories of this paper are: supr-con
6
The categories of this paper are: astro-ph
35
The categories of this paper are: mtrl-th
15
The categories of this paper are: nucl-ex
14
The categories of this paper are: math-ph
36
The categories of this paper are: cmp-lg
30
The categories of this paper are: q-alg
21
The categories of this paper are: adap-org