M. Dorodnyi

Homogenization of one-dimensional hyperbolic equations with corrector

We consider an elliptic differential operator $A_\varepsilon=- \frac{d}{dx} g(\frac x\varepsilon) \frac{d}{dx}$, $\varepsilon > 0$, with a periodic coefficient that acts in $L_2(\mathbb{R})$. We study the behaviour of solutions of the Cauchy problem for the hyperbolic equation $partial_\tau^2 w_\varepsilon (x,\tau)=- (...