$L^2$-estimates of error in homogenization of parabolic equations with correctors taken into account

S. E. Pastukhova

MIREA — Russian Technological University, Moscow, Russia

Abstract: We consider second-order parabolic equations with bounded measurable $\varepsilon$-periodic coefficients. To solve the Cauchy problem in the layer $\mathbb{R}^d\times(0,T)$ with the nonhomogeneous equation, we obtain approximations in the norm $\|\cdot\|_{L^2(\mathbb{R}^d\times(0,T))}$ with remainder of order $\varepsilon^2$ as $\varepsilon\to 0.$

Keywords: parabolic equations, homogenization of solutions, homogenization error, corrector.

UDC: 517.97

DOI: 10.22363/2413-3639-2023-69-1-134-151