# American Institute of Mathematical Sciences

May  2009, 3(2): 309-317. doi: 10.3934/ipi.2009.3.309

## Unique continuation property for the elasticity with general residual stress

 1 Department of Mathematics, University of Washington, Seattle, WA 98195-4350 2 Department of Mathematics, TIMS and CTS(Taipei), National Taiwan University, Taipei 106, Taiwan

Received  January 2009 Revised  March 2009 Published  May 2009

We prove the unique continuation property for the isotropic elasticity system with arbitrarily large residual stress. This work improves the result obtained in [10] where the residual stress is assumed to be small.
Citation: Gunther Uhlmann, Jenn-Nan Wang. Unique continuation property for the elasticity with general residual stress. Inverse Problems & Imaging, 2009, 3 (2) : 309-317. doi: 10.3934/ipi.2009.3.309
 [1] Muriel Boulakia. Quantification of the unique continuation property for the nonstationary Stokes problem. Mathematical Control & Related Fields, 2016, 6 (1) : 27-52. doi: 10.3934/mcrf.2016.6.27 [2] Laurent Bourgeois. Quantification of the unique continuation property for the heat equation. Mathematical Control & Related Fields, 2017, 7 (3) : 347-367. doi: 10.3934/mcrf.2017012 [3] Nanhee Kim. Uniqueness and Hölder type stability of continuation for the linear thermoelasticity system with residual stress. Evolution Equations & Control Theory, 2013, 2 (4) : 679-693. doi: 10.3934/eect.2013.2.679 [4] Guojie Zheng, Dihong Xu, Taige Wang. A unique continuation property for a class of parabolic differential inequalities in a bounded domain. Communications on Pure & Applied Analysis, 2021, 20 (2) : 547-558. doi: 10.3934/cpaa.2020280 [5] Agnid Banerjee. A note on the unique continuation property for fully nonlinear elliptic equations. Communications on Pure & Applied Analysis, 2015, 14 (2) : 623-626. doi: 10.3934/cpaa.2015.14.623 [6] Rebecca Vandiver. Effect of residual stress on peak cap stress in arteries. Mathematical Biosciences & Engineering, 2014, 11 (5) : 1199-1214. doi: 10.3934/mbe.2014.11.1199 [7] Peng Gao. Unique continuation property for stochastic nonclassical diffusion equations and stochastic linearized Benjamin-Bona-Mahony equations. Discrete & Continuous Dynamical Systems - B, 2019, 24 (6) : 2493-2510. doi: 10.3934/dcdsb.2018262 [8] Peng Gao. Carleman estimates and Unique Continuation Property for 1-D viscous Camassa-Holm equation. Discrete & Continuous Dynamical Systems, 2017, 37 (1) : 169-188. doi: 10.3934/dcds.2017007 [9] Giovanni Covi, Keijo Mönkkönen, Jesse Railo. Unique continuation property and Poincaré inequality for higher order fractional Laplacians with applications in inverse problems. Inverse Problems & Imaging, 2021, 15 (4) : 641-681. doi: 10.3934/ipi.2021009 [10] José G. Llorente. Mean value properties and unique continuation. Communications on Pure & Applied Analysis, 2015, 14 (1) : 185-199. doi: 10.3934/cpaa.2015.14.185 [11] Moniba Shams. Wave-propagation in an incompressible hollow elastic cylinder with residual stress. Discrete & Continuous Dynamical Systems - S, 2020, 13 (10) : 2877-2904. doi: 10.3934/dcdss.2020123 [12] Zhongqi Yin. A quantitative internal unique continuation for stochastic parabolic equations. Mathematical Control & Related Fields, 2015, 5 (1) : 165-176. doi: 10.3934/mcrf.2015.5.165 [13] A. Alexandrou Himonas, Gerard Misiołek, Feride Tiǧlay. On unique continuation for the modified Euler-Poisson equations. Discrete & Continuous Dynamical Systems, 2007, 19 (3) : 515-529. doi: 10.3934/dcds.2007.19.515 [14] Can Zhang. Quantitative unique continuation for the heat equation with Coulomb potentials. Mathematical Control & Related Fields, 2018, 8 (3&4) : 1097-1116. doi: 10.3934/mcrf.2018047 [15] Xuping Xie, Feng Bao, Thomas Maier, Clayton Webster. Analytic continuation of noisy data using Adams Bashforth residual neural network. Discrete & Continuous Dynamical Systems - S, 2021  doi: 10.3934/dcdss.2021088 [16] Ihyeok Seo. Carleman estimates for the Schrödinger operator and applications to unique continuation. Communications on Pure & Applied Analysis, 2012, 11 (3) : 1013-1036. doi: 10.3934/cpaa.2012.11.1013 [17] Jan Boman. Unique continuation of microlocally analytic distributions and injectivity theorems for the ray transform. Inverse Problems & Imaging, 2010, 4 (4) : 619-630. doi: 10.3934/ipi.2010.4.619 [18] Mouhamed Moustapha Fall, Veronica Felli. Unique continuation properties for relativistic Schrödinger operators with a singular potential. Discrete & Continuous Dynamical Systems, 2015, 35 (12) : 5827-5867. doi: 10.3934/dcds.2015.35.5827 [19] Roberto Triggiani. Unique continuation of boundary over-determined Stokes and Oseen eigenproblems. Discrete & Continuous Dynamical Systems - S, 2009, 2 (3) : 645-677. doi: 10.3934/dcdss.2009.2.645 [20] Victor Isakov, Nanhee Kim. Weak Carleman estimates with two large parameters for second order operators and applications to elasticity with residual stress. Discrete & Continuous Dynamical Systems, 2010, 27 (2) : 799-825. doi: 10.3934/dcds.2010.27.799

2020 Impact Factor: 1.639