116
Views
0
CrossRef citations to date
0
Altmetric
Articles

Recovering density for the Mindlin–Timoshenko system by means of a single boundary measurement

, &
Pages 1682-1698 | Received 28 Feb 2021, Accepted 10 Oct 2021, Published online: 27 Oct 2021

References

  • The collected papers of Stephen P. Timoshenko. McGraw–Hill Book Company, Inc; 1953.
  • Sare HDF. On the stability of Mindlin-Timoshenko plates. Quart Appl Math. 2009;LXVII(2):249.
  • Lagnese JE. Boundary stabilization of thin plates. Philadelphia: SIAM; 1989. (SIAM studies in applied mathematics; 10).
  • Bukhgeim A, Klibanov M. Uniqueness in the large of a class of multidimensional inverse problems. Dokl Akad Nauk SSSR. 1981;260:269–272.
  • Bellassoued M, Yamamoto M. Carleman estimates and applications to inverse problems for hyperbolic systems. Tokyo: Springer; 2017.
  • Isakov V. Inverse problems for partial differential equations. 2nd ed. New York (NY): Springer; 2006. (Applied mathematical sciences; 127).
  • Isakov V. Inverse source problems. Providence (RI): American Mathematical Society; 1990. (Mathematical surveys and monographs; 34).
  • Klibanov M. Carleman estimates for coefficient inverse problems and numerical applications. VSP, Utrecht; 2004. (Inverse and Ill-Posed Problems Series).
  • Liu S, Triggiani R. Boundary control and boundary inverse theory for non-homogeneous second order hyperbolic equations: a common Carleman estimates approach. American Institute of Mathematical Sciences; 2011. Chapter 3, (Applied Mathematics).
  • Uniqueness and stability in the Cauchy problem for Maxwell and elasticity systems. 2002. (Studies in mathematics and its applications).
  • Pedersen M. Well posedness and regularity of the controlled Mindlin–Timoshenko plate model. Int J Pure Appl Math. 2007;40(2):273–289.
  • Pei P, Rammaha MA, Toundykov D. Well-posedness and stability of a Mindlin-Timoshenko plate model with damping and sources. In: Mityushev VV and Ruzhansky MV, editors. Current trends in analysis and its applications. Switzerland: Springer International; 2015. p. 307–314. ISAAC Congress.
  • Rammaha MA, Pei P, Toundykov D. Global well-posedness and stability of semilinear Mindlin–Timoshenko system. J Math Anal Appl. 2014;418:535–568.
  • Tebou L. Indirect stabilization of a Mindlin-Timoshenko plate. J Math Anal Appl. 1880–1891;449:2017.
  • Lasiecka I, Triggiani R, Zhang X. Nonconservative wave equations with unobserved Neumann B.C.: global uniqueness and observability in one shot. Contemp Math. 2000;268:227–326.
  • Triggiani R, Yao PF. Carleman estimates with no lower-order terms for general Riemann wave equations. Global uniqueness and observability in one shot. Appl Math Optim. 2002;46:331–375.
  • DoCarmo MP. Riemannian geometry. Boston (MA): Birkhäuser; 1992.
  • Yao P. On the observability inequalities for exact controllability of wave equations with variable coefficients. Siam J Control Optim. 1999 Jun;37:1568–1599.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.