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
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DOI：
10.1080/00036811.2010.534731
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发表时间：
2012-01
影响因子：
1.1
通讯作者：
M. Bellassoued;Masahiro Yamamoto
中科院分区：
文献类型：
--
作者：
M. Bellassoued;Masahiro Yamamoto
本文证明了一类黎曼流形中二阶双曲算子的二阶大参数Carleman估计。如果考虑的函数在边界∂（x (0， T)）上消失，则我们的Carleman估计在整个柱面域（x (0， T)）内成立，与权函数生成的水平集无关。用黎曼流形中张量场的演算直接证明了这一点。然后，由于第二个较大参数的依赖性，我们还证明了(i)耦合抛物-双曲系统（ii）热弹性板系统（iii）带残余应力的热弹性系统的Carleman估计。
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 × (0, T) independent of the level set generated by a weight function if functions under consideration vanish on boundary ∂(ℳ × (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.