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

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  • 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.
    Mathematics Subject Classification: Primary: 35J56, 35B45; Secondary: 35L50, 93D15, 35Q61.


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