[Author]
 Dorodnyi, M. A.

[Title]
 Homogenization of one-dimensional hyperbolic equations with corrector

[AMS Subj-class]
 35B27 Homogenization; partial differential equations in media with periodic structure

[Keywords]
 periodic differential operators, hyperbolic equations, spectral bands, homogenization,
 effective operator, corrector, operator error estimates

[Abstract]
 We consider an elliptic differential operator
 $A_\varepsilon = - \frac{d}{dx} g(x/\varepsilon) \frac{d}{dx}$, $ \varepsilon > 0$,
 with periodic coefficients acting in $L_2(\mathbb{R})$. The behavior of the solution
 of the Cauchy problem for the hyperbolic equation
 $\partial_\tau^2 u_\varepsilon (x,\tau) = - (A_\varepsilon u_\varepsilon) (x,\tau)$
 is studied, as $\varepsilon \to 0$. We obtain an approximation of the solution
 $u_\varepsilon (\cdot,\tau)$ in the $L_2 (\mathbb{R})$-norm with error $O(\varepsilon^2)$.
 In this approximation a corrector is taken into account.

[Comments]
 Russian, 29 pp.

[Contact e-mail]
 mdorodni@yandex.ru