Differential and Integral Equations

Homogenization of a hyperbolic equation with highly contrasting diffusivity coefficients

A.K. Nandakumaran and Ali Sili

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Abstract

We study a hyperbolic problem in the framework of periodic homogenization assuming a high contrast between the diffusivity coefficients of the two components $M_{\varepsilon}$ and $ B_{\varepsilon}$ of the heterogeneous medium. There are three regimes depending on the ratio between the size of the period and the amplitude ${\alpha_{\varepsilon}}$ of the diffusivity in $ B_{\varepsilon}$. For the critical regime $ \alpha_{\varepsilon} \simeq {\varepsilon}$, the limit problem is a strongly coupled system involving both the macroscopic and the microscopic variables. We also include the results in the non critical case.

Article information

Source
Differential Integral Equations Volume 29, Number 1/2 (2016), 37-54.

Dates
First available in Project Euclid: 24 November 2015

Permanent link to this document
https://projecteuclid.org/euclid.die/1448323252

Mathematical Reviews number (MathSciNet)
MR3450748

Zentralblatt MATH identifier
1349.35027

Subjects
Primary: 35B27: Homogenization; equations in media with periodic structure [See also 74Qxx, 76M50] 78M35: Asymptotic analysis 80M35: Asymptotic analysis

Citation

Nandakumaran, A.K.; Sili, Ali. Homogenization of a hyperbolic equation with highly contrasting diffusivity coefficients. Differential Integral Equations 29 (2016), no. 1/2, 37--54. https://projecteuclid.org/euclid.die/1448323252.


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