A Carleman estimate for the linear shallow shell equation and an inverse source problem

Previous Article
Isometric immersions into the Minkowski spacetime for Lorentzian manifolds with limited regularity
DCDS Home
This Issue
Next Article
The initial-boundary value problem on a strip for the equation of time-like extremal surfaces

January & February 2009, 23(1&2): 367-380. doi: 10.3934/dcds.2009.23.367

A Carleman estimate for the linear shallow shell equation and an inverse source problem

Shumin Li ^1, , Masahiro Yamamoto ^1, and Bernadette Miara ^2,

1.	Department of Mathematical Sciences, The University of Tokyo, Komaba Meguro Tokyo 153-8914, Japan, Japan
2.	Laboratoire de Modélisation et Simulation Numérique, École Supérieure d'Ingenieurs en Électrotechnique et Électronique, Cité Descartes, 2 Boulevard Blaise Pascal, 93160 Noisy-le-Grand Cedex, France

Received December 2007 Revised March 2008 Published September 2008

Abstract
Related Papers

We consider an elastic bi-dimensional body whose reference configuration is a shallow shell. We establish a Carleman estimate for the linear shallow shell equations and apply it to prove a conditional stability for an inverse problem of determining external source terms by observations of displacement in a neighbourhood of the boundary over a time interval.

Keywords: inverse source problem, conditional stability, Carleman estimate, shallow shell.

Mathematics Subject Classification: Primary: 34A55, ; Secondary: 34A30.

Citation: Shumin Li, Masahiro Yamamoto, Bernadette Miara. A Carleman estimate for the linear shallow shell equation and an inverse source problem. Discrete & Continuous Dynamical Systems - A, 2009, 23 (1&2) : 367-380. doi: 10.3934/dcds.2009.23.367

[1]	Lucie Baudouin, Emmanuelle Crépeau, Julie Valein. Global Carleman estimate on a network for the wave equation and application to an inverse problem. Mathematical Control & Related Fields, 2011, 1 (3) : 307-330. doi: 10.3934/mcrf.2011.1.307
[2]	Atsushi Kawamoto. Hölder stability estimate in an inverse source problem for a first and half order time fractional diffusion equation. Inverse Problems & Imaging, 2018, 12 (2) : 315-330. doi: 10.3934/ipi.2018014
[3]	Aymen Jbalia. On a logarithmic stability estimate for an inverse heat conduction problem. Mathematical Control & Related Fields, 2019, 9 (2) : 277-287. doi: 10.3934/mcrf.2019014
[4]	Peijun Li, Ganghua Yuan. Increasing stability for the inverse source scattering problem with multi-frequencies. Inverse Problems & Imaging, 2017, 11 (4) : 745-759. doi: 10.3934/ipi.2017035
[5]	Peng-Fei Yao. On shallow shell equations. Discrete & Continuous Dynamical Systems - S, 2009, 2 (3) : 697-722. doi: 10.3934/dcdss.2009.2.697
[6]	Peng Gao. Global Carleman estimate for the Kawahara equation and its applications. Communications on Pure & Applied Analysis, 2018, 17 (5) : 1853-1874. doi: 10.3934/cpaa.2018088
[7]	Frederic Weidling, Thorsten Hohage. Variational source conditions and stability estimates for inverse electromagnetic medium scattering problems. Inverse Problems & Imaging, 2017, 11 (1) : 203-220. doi: 10.3934/ipi.2017010
[8]	Kenichi Sakamoto, Masahiro Yamamoto. Inverse source problem with a final overdetermination for a fractional diffusion equation. Mathematical Control & Related Fields, 2011, 1 (4) : 509-518. doi: 10.3934/mcrf.2011.1.509
[9]	Yuxuan Gong, Xiang Xu. Inverse random source problem for biharmonic equation in two dimensions. Inverse Problems & Imaging, 2019, 13 (3) : 635-652. doi: 10.3934/ipi.2019029
[10]	Emine Kaya, Eugenio Aulisa, Akif Ibragimov, Padmanabhan Seshaiyer. A stability estimate for fluid structure interaction problem with non-linear beam. Conference Publications, 2009, 2009 (Special) : 424-432. doi: 10.3934/proc.2009.2009.424
[11]	J. F. Padial. Existence and estimate of the location of the free-boundary for a non local inverse elliptic-parabolic problem arising in nuclear fusion. Conference Publications, 2011, 2011 (Special) : 1176-1185. doi: 10.3934/proc.2011.2011.1176
[12]	Guanghui Hu, Peijun Li, Xiaodong Liu, Yue Zhao. Inverse source problems in electrodynamics. Inverse Problems & Imaging, 2018, 12 (6) : 1411-1428. doi: 10.3934/ipi.2018059
[13]	Chunpeng Wang, Yanan Zhou, Runmei Du, Qiang Liu. Carleman estimate for solutions to a degenerate convection-diffusion equation. Discrete & Continuous Dynamical Systems - B, 2018, 23 (10) : 4207-4222. doi: 10.3934/dcdsb.2018133
[14]	Pedro Caro. On an inverse problem in electromagnetism with local data: stability and uniqueness. Inverse Problems & Imaging, 2011, 5 (2) : 297-322. doi: 10.3934/ipi.2011.5.297
[15]	Michele Di Cristo. Stability estimates in the inverse transmission scattering problem. Inverse Problems & Imaging, 2009, 3 (4) : 551-565. doi: 10.3934/ipi.2009.3.551
[16]	Wenxiong Chen, Congming Li. A priori estimate for the Nirenberg problem. Discrete & Continuous Dynamical Systems - S, 2008, 1 (2) : 225-233. doi: 10.3934/dcdss.2008.1.225
[17]	Zhousheng Ruan, Sen Zhang, Sican Xiong. Solving an inverse source problem for a time fractional diffusion equation by a modified quasi-boundary value method. Evolution Equations & Control Theory, 2018, 7 (4) : 669-682. doi: 10.3934/eect.2018032
[18]	Jingzhi Li, Masahiro Yamamoto, Jun Zou. Conditional Stability and Numerical Reconstruction of Initial Temperature. Communications on Pure & Applied Analysis, 2009, 8 (1) : 361-382. doi: 10.3934/cpaa.2009.8.361
[19]	Albert Clop, Daniel Faraco, Alberto Ruiz. Stability of Calderón's inverse conductivity problem in the plane for discontinuous conductivities. Inverse Problems & Imaging, 2010, 4 (1) : 49-91. doi: 10.3934/ipi.2010.4.49
[20]	Li Liang. Increasing stability for the inverse problem of the Schrödinger equation with the partial Cauchy data. Inverse Problems & Imaging, 2015, 9 (2) : 469-478. doi: 10.3934/ipi.2015.9.469

2017 Impact Factor: 1.179

American Institute of Mathematical Sciences