Bellassoued, Mourad; Yamamoto, Masahiro Carleman estimate with second large parameter for second order hyperbolic operators in a Riemannian manifold and applications in thermoelasticity cases. (English) Zbl 1235.35051 Appl. Anal. 91, No. 1-2, 35-67 (2012). 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. Cited in 12 Documents 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 Keywords:Carleman estimates; second large parameter; hyperbolic equation; thermoelasticity system; coupled parabolic-hyperbolic system; thermoelastic plate system; thermoelasticity system with residual stress. PDF BibTeX XML Cite \textit{M. Bellassoued} and \textit{M. Yamamoto}, Appl. Anal. 91, No. 1--2, 35--67 (2012; Zbl 1235.35051) Full Text: DOI References: [1] Carleman T, Ark. Math. Astr. Fys. 2 pp 1– (1939) [2] Hörmander L, Linear Partial Differential Operators (1963) [3] Isakov V, Inverse Problems for Partial Differential Equations (2006) [4] Lavrent’ev MM, Ill-posed Problems of Mathematical Physics and Analysis (1986) [5] Tataru D, J. Math. Pures Appl. 75 pp 367– (1996) [6] DOI: 10.1080/00036810802369249 · Zbl 1149.35404 · doi:10.1080/00036810802369249 [7] Imanuvilov OY, Asymptot. Anal. 32 pp 185– (2002) [8] DOI: 10.1007/s00245-002-0751-5 · Zbl 1030.35018 · doi:10.1007/s00245-002-0751-5 [9] Klibanov MV, Carleman Estimates for Coefficient Inverse Problems and Numerical Applications (2004) [10] Bukhgeim AL, Soviet Math. Dokl. 24 pp 244– (1981) [11] DOI: 10.1080/0003681042000221678 · Zbl 1069.35035 · doi:10.1080/0003681042000221678 [12] DOI: 10.1016/j.matpur.2005.02.004 · Zbl 1091.35112 · doi:10.1016/j.matpur.2005.02.004 [13] DOI: 10.1081/PDE-100106139 · Zbl 0985.35108 · doi:10.1081/PDE-100106139 [14] DOI: 10.1088/0266-5611/14/5/009 · Zbl 0992.35110 · doi:10.1088/0266-5611/14/5/009 [15] DOI: 10.1088/0266-5611/8/4/009 · Zbl 0755.35151 · doi:10.1088/0266-5611/8/4/009 [16] DOI: 10.1088/0266-5611/25/12/123013 · Zbl 1194.35512 · doi:10.1088/0266-5611/25/12/123013 [17] Isakov V, Appl. Math. 35 pp 447– (2008) [18] DOI: 10.1007/978-0-387-85652-0 · Zbl 1152.46001 · doi:10.1007/978-0-387-85652-0 [19] DOI: 10.1006/jmaa.2000.6903 · Zbl 0973.35044 · doi:10.1006/jmaa.2000.6903 [20] Eller M, Contemp. Math. 268 pp 117– (2000) [21] Jost J, Riemannian Geometry and Geometric Analysis (1995) [22] Hebey E, Sobolev Spaces on Riemannian manifolds, Lecture Notes in Mathematics, Vol. 1635 (1996) · Zbl 0866.58068 [23] DOI: 10.1006/jmaa.1999.6348 · Zbl 0931.35022 · doi:10.1006/jmaa.1999.6348 [24] DOI: 10.1016/j.aml.2007.07.032 · Zbl 1152.35512 · doi:10.1016/j.aml.2007.07.032 [25] DOI: 10.1080/00036810802428995 · Zbl 1181.35141 · doi:10.1080/00036810802428995 [26] DOI: 10.1201/9781420036220 · doi:10.1201/9781420036220 [27] Fursikov AV, Controllability of Evolution Equations (1996) [28] Albano P, Electron. J. Differ. Equ. 2000 pp 1– (2000) [29] DOI: 10.1088/0266-5611/14/2/007 · Zbl 0898.35104 · doi:10.1088/0266-5611/14/2/007 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.