Sobolev Spaces in Mathematics III

Isakov, Victor

doi:10.1007/978-0-387-85652-0

International Mathematical Series

2009

DOI: 10.1007/978-0-387-85652-0

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Sobolev Spaces in Mathematics III

Victor Isakov¹

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2024

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Carleman estimate with second large parameter for second order hyperbolic operators in a Riemannian manifold and applications in thermoelasticity cases

Bellassoued

Yamamoto

2012

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In this article we prove a Carleman estimate with second large parameter for a second order hyperbolic operator in a Riemannian manifold M. Our Carleman estimate holds in the whole cylindrical domain M Â (0, T ) independent of the level set generated by a weight function if functions under consideration vanish on boundary @(M Â (0, T )). The proof is direct by using calculus of tensor fields in a Riemannian manifold. Then, thanks to the dependency of the second larger parameter, we prove Carleman estimates also for (i) a coupled parabolic-hyperbolic system (ii) a thermoelastic plate system (iii) a thermoelasticity system with residual stress.

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Carleman estimate with second large parameter for second order hyperbolic operators in a Riemannian manifold and applications in thermoelasticity cases

Bellassoued

Yamamoto

2012

Applicable Analysis

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Generalizations of Sobolev classes to the metric and topological cases

Romsnovskii

2024

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Sobolev Spaces in Mathematics III

Cited by 2 publications

References 28 publications

Carleman estimate with second large parameter for second order hyperbolic operators in a Riemannian manifold and applications in thermoelasticity cases

Carleman estimate with second large parameter for second order hyperbolic operators in a Riemannian manifold and applications in thermoelasticity cases

Generalizations of Sobolev classes to the metric and topological cases

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