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Carleman estimate with second large parameter for second order hyperbolic operators in a Riemannian manifold and applications in thermoelasticity cases. (English) Zbl 1235.35051
Summary: We prove a Carleman estimate with second large parameter for a second order hyperbolic operator in a Riemannian manifold \(\mathcal M\). Our Carleman estimate holds in the whole cylindrical domain \(\mathcal M\times (0, T)\) independent of the level set generated by a weight function if functions under consideration vanish on boundary \(\partial (\mathcal M\times (0, T))\). 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.

MSC:
35B45 A priori estimates in context of PDEs
35B60 Continuation and prolongation of solutions to PDEs
74F05 Thermal effects in solid mechanics
58J45 Hyperbolic equations on manifolds
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