Evolution Equations and Control Theory (EECT)

Carleman estimates for some anisotropic elasticity systems and applications

Pages: 141 - 154, Volume 1, Issue 1, June 2012      doi:10.3934/eect.2012.1.141

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Victor Isakov - Wichita State University, 1845 Fairmount, Wichita, KS, 67260-0033, United States (email)

Abstract: We show that under some conditions one can obtain Carleman type estimates for the transversely isotropic elasticity system with residual stress. We consider both time dependent and static cases. The main idea is to reduce this system to a principally upper triangular one and the main technical tool is Carleman estimates with two large parameters for general second order partial differential operators.

Keywords:  Partial differential equations, improperly posed problems, Cauchy problem, Carleman estimates, linear anisotropic elasticity.
Mathematics Subject Classification:  Primary: 35R25; Secondary: 35B60; 74B60.

Received: October 2011;      Revised: February 2012;      Available Online: March 2012.