Homogenization and correctors for the hyperbolic problems        with imperfect interfaces via the periodic unfolding method

Zhanying Yang

doi:10.3934/cpaa.2014.13.249

Article Contents

2014, Volume 13, Issue 1: 249-272. Doi: 10.3934/cpaa.2014.13.249

This issue Previous Article Least energy solutions for semilinear Schrödinger equations involving critical growth and indefinite potentials Next Article Global well-posedness of some high-order semilinear wave and Schrödinger type equations with exponential nonlinearity

Homogenization and correctors for the hyperbolic problems with imperfect interfaces via the periodic unfolding method

Zhanying Yang^1,

1.
Department of Mathematics, South-Central University for Nationalities, Wuhan 430074

Received: December 2012

Revised: June 2013

Published: January 2014

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Abstract

In this paper, we study the homogenization and corrector results for the hyperbolic problem in a two-component composite with $\varepsilon$-periodic connected inclusions. The condition prescribed on the interface is that a jump of the solution is proportional to the conormal derivatives via a function of order $\varepsilon^\gamma$ ($\gamma < -1$). The main ingredient of the proof of our main theorems is the time-dependent periodic unfolding method in two-component domains. Our homogenization results recover those of the corresponding case in [Donato, Faella and Monsurrò, J. Math. Pures Appl. 87 (2007), pp. 119-143]. We also derive the corresponding corrector results.

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Mathematics Subject Classification: Primary: 35B27; Secondary: 35L05, 82B24.

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