# Homogenization of the first initial boundary-value problem for parabolic systems: operator error estimates

@article{Meshkova2018HomogenizationOT, title={Homogenization of the first initial boundary-value problem for parabolic systems: operator error estimates}, author={Yu. M. Meshkova and Tatiana Suslina}, journal={St. Petersburg Mathematical Journal}, year={2018} }

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 $B_{D,\varepsilon}$, $0 0$, 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…

## 6 Citations

Homogenization of the Dirichlet problem for elliptic systems: Two-parametric error estimates

- Mathematics
- 2017

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 study a selfadjoint matrix elliptic second order differential operator…

Homogenization of periodic parabolic systems in the $L_2(\mathbb {R}^d)$-norm with the corrector taken into account

- MathematicsSt. Petersburg Mathematical Journal
- 2020

In $L_2(\mathbb{R}^d;\mathbb{C}^n)$, consider a self-adjoint matrix second order elliptic differential operator $\mathcal{B}_\varepsilon$, $0<\varepsilon \leqslant 1$. The principal part of the…

Variations on the theme of the Trotter-Kato theorem for homogenization of periodic hyperbolic systems

- Mathematics, Computer Science
- 2019

The proof of the Trotter-Kato theorem is adopted by introduction of some correction term and hyperbolic results from elliptic ones are derived from elliptIC ones.

On homogenization of periodic hyperbolic systems in $L_2(\mathbb{R}^d;\mathbb{C}^n)$. Variations on the theme of the Trotter-Kato theorem

- Mathematics
- 2019

In L2(R d;Cn), we consider a matrix elliptic second order differential operator Bε > 0. Coefficients of the operator Bε are periodic with respect to some lattice in Rd and depend on x/ε. We study the…

On homogenization of the first initial-boundary value problem for periodic hyperbolic systems

- MathematicsApplicable Analysis
- 2018

ABSTRACT Let be a bounded domain of class . In , we consider a self-adjoint matrix strongly elliptic second-order differential operator , , with the Dirichlet boundary condition. The coefficients of…

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