# American Institute of Mathematical Sciences

December  2012, 1(2): 271-296. doi: 10.3934/eect.2012.1.271

## Carleman estimates for elliptic boundary value problems with applications to the stablization of hyperbolic systems

 1 Department of Mathematics, Georgetown University, Washington, DC 20057, United States 2 Department of Mathematics, University of Nebraska-Lincoln, Lincoln, NE 68588, United States

Received  July 2012 Revised  September 2012 Published  October 2012

A Carleman estimate for some first-order elliptic systems is established. This estimate is extended to elliptic boundary value problems provided the boundary condition satisfies a Lopatinskii-type requirement. Based on these estimates conservative hyperbolic systems of first order can be stabilized with a logarithmic decay rate by introducing a localized interior dissipation. The support of the dissipative term does not need to satisfy a geometric condition.
Citation: Matthias Eller, Daniel Toundykov. Carleman estimates for elliptic boundary value problems with applications to the stablization of hyperbolic systems. Evolution Equations & Control Theory, 2012, 1 (2) : 271-296. doi: 10.3934/eect.2012.1.271
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