Strong convergence of the solutions of the linear elasticity and uniformity of asymptotic expansions in the presence of small inclusions

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:254

Article

Ammari, Habib¹  Kang, Hyeonbae²  Kim, Kyoungsun²  Lee, Hyundae² 

[1] Ecole Normale Super, Dept Math & Applicat, F-75005 Paris, France

[2] Inha Univ, Dept Math, Inchon 402751, South Korea

关键词: Strong convergence;    Lame parameters;    High contrast;    Asymptotic expansion;    Uniformity;   

DOI  :  10.1016/j.jde.2013.03.008

来源: Elsevier

【 摘 要 】

We consider the Lame system of linear elasticity when the inclusion has the extreme elastic constants. We show that the solutions to the Lame system converge in appropriate H-1-norms when the shear modulus tends to infinity (the other modulus, the compressional modulus is fixed), and when the bulk modulus and the shear Modulus tend to zero. Using this result, we show that the asymptotic expansion of the displacement Vector in the presence of small inclusion is uniform with respect to Lame parameters. (C) 2013 Elsevier Inc. All rights reserved.

【 授权许可】

Free