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Applicable Analysis
An International Journal
Volume 88, 2009 - Issue 5: Inverse Problems
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Original Articles

Inverse problem for a parabolic system with two components by measurements of one component

Assia Benabdallah Laboratoire d'Analyse Topologie Probabilités, CNRS UMR 6632, Université d'Aix-Marseille, Marseille, FranceCorrespondence[email protected]
,
Michel Cristofol Laboratoire d'Analyse Topologie Probabilités, CNRS UMR 6632, Université d'Aix-Marseille, Marseille, France
,
Patricia Gaitan Laboratoire d'Analyse Topologie Probabilités, CNRS UMR 6632, Université d'Aix-Marseille, Marseille, France
&
Masahiro Yamamoto Department of Mathematics, University of Tokyo, Tokyo, Japan
Pages 683-709 | Received 09 Sep 2008, Accepted 13 Oct 2008, Published online: 22 Jul 2009

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Xiaomin Zhu & Fangfang Dou. (2023) Conditional stability of coefficients inverse problem for strongly coupled Schrödinger equations. Applicable Analysis 102:5, pages 1294-1311.
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Abir Amri, Mourad Bellassoued, Moncef Mahjoub & Nejib zemzemi. (2023) Analysis of the heart-torso conductivity parameters recovery inverse problem in cardiac electrophysiology ECG modelling. Applicable Analysis 102:2, pages 494-523.
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K. Sakthivel, A. Arivazhagan & N. Barani Balan. (2022) Inverse problem for a Cahn–Hilliard type system modeling tumor growth. Applicable Analysis 101:3, pages 858-890.
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Michel Cristofol, Patricia Gaitan, Hichem Ramoul & Masahiro Yamamoto. (2012) Identification of two coefficients with data of one component for a nonlinear parabolic system. Applicable Analysis 91:11, pages 2073-2081.
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Michel Cristofol & Eric Soccorsi. (2011) Stability estimate in an inverse problem for non-autonomous magnetic Schrödinger equations. Applicable Analysis 90:10, pages 1499-1520.
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Laure Cardoulis & Michel Cristofol. An inverse problem for a generalized FitzHugh–Nagumo type system. Applicable Analysis 0:0, pages 1-13.
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Laure Cardoulis. (2023) An inverse problem for a hyperbolic system in a bounded domain. Comptes Rendus. Mathématique 361:G3, pages 653-665.
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Fangfang Dou & Masahiro Yamamoto. (2019) Logarithmic stability for a coefficient inverse problem of coupled Schrödinger equations. Inverse Problems 35:7, pages 075006.
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Yassine Abidi, Mourad Bellassoued, Moncef Mahjoub & Nejib Zemzemi. (2019) Ionic parameters identification of an inverse problem of strongly coupled PDE’s system in cardiac electrophysiology using Carleman estimates. Mathematical Modelling of Natural Phenomena 14:2, pages 202.
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Nicolás Carreño, Roberto Morales & Axel Osses. (2018) Potential reconstruction for a class of hyperbolic systems from incomplete measurements. Inverse Problems 34:8, pages 085005.
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D. G. Orlovsky & S. I. Piskarev. (2018) On Approximation of Coefficient Inverse Problems for Differential Equations in Functional Spaces. Journal of Mathematical Sciences 230:6, pages 823-906.
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Patricia Gaitan & Hadjer Ouzzane. (2017) Stability result for two coefficients in a coupled hyperbolic-parabolic system. Journal of Inverse and Ill-posed Problems 25:3, pages 265-286.
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Bin Wu & Jun Yu. (2017) Hölder stability of an inverse problem for a strongly coupled reaction-diffusion system. IMA Journal of Applied Mathematics, pages hxw058.
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I. Dimov, J. Kandilarov, V. Todorov & L. Vulkov. Numerical determination of the right-hand side of parabolic systems with point measurements. Numerical determination of the right-hand side of parabolic systems with point measurements.
Jamila Lassoued, Moncef Mahjoub & Néjib Zemzemi. (2016) Stability results for the parameter identification inverse problem in cardiac electrophysiology. Inverse Problems 32:11, pages 115002.
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Hichem Ramoul. (2014) Carleman estimate for a one-dimensional system of m coupled parabolic PDEs with BV diffusion coefficients. Boundary Value Problems 2014:1.
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Assia Benabdallah, Michel Cristofol, Patricia Gaitan & Luz Teresa. (2013) Controllability to trajectories for some parabolic systems of three and two equations by one control force. Mathematical Control and Related Fields 4:1, pages 17-44.
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Bin Wu, Qun Chen & Zewen Wang. (2013) Uniqueness and stability of an inverse problem for a phase field model using data from one component. Computers & Mathematics with Applications 66:10, pages 2126-2138.
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Mourad Bellassoued & Masahiro Yamamoto. (2013) Carleman estimate and inverse source problem for Biot’s equations describing wave propagation in porous media. Inverse Problems 29:11, pages 115002.
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Bin Wu, Jun Yu & Zewen Wang. (2013) Uniqueness and stability of an inverse kernel problem for type III thermoelasticity. Journal of Mathematical Analysis and Applications 402:1, pages 242-254.
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Michel Cristofol, Patricia Gaitan, Kati Niinim?ki & Olivier Poisson. (2013) Inverse problem for a coupled parabolic system with discontinuous conductivities: One-dimensional case. Inverse Problems and Imaging 7:1, pages 159-182.
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Louis Tebou. (2012) Sharp Observability Estimates for a System of Two Coupled Nonconservative Hyperbolic Equations. Applied Mathematics & Optimization 66:2, pages 175-207.
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Bin Wu & Jijun Liu. (2012) Determination of an unknown source for a thermoelastic system with a memory effect. Inverse Problems 28:9, pages 095012.
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Mourad Bellassoued, Michel Cristofol & Eric Soccorsi. (2012) Inverse boundary value problem for the dynamical heterogeneous Maxwell's system. Inverse Problems 28:9, pages 095009.
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Lionel Roques & Michel Cristofol. (2012) The inverse problem of determining several coefficients in a nonlinear Lotka–Volterra system. Inverse Problems 28:7, pages 075007.
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Michael V Klibanov. (2011) Uniqueness of an inverse problem with single measurement data generated by a plane wave in partial finite differences. Inverse Problems 27:11, pages 115005.
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Michel Cristofol, Jimmy Garnier, François Hamel & Lionel Roques. (2011) Uniqueness from pointwise observations in a multi-parameter inverse problem. Communications on Pure and Applied Analysis 11:1, pages 173-188.
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Bin Wu & Jijun Liu. (2011) Conditional stability and uniqueness for determining two coefficients in a hyperbolic–parabolic system. Inverse Problems 27:7, pages 075013.
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Masahiro Yamamoto. (2011) Carleman estimates and an inverse heat source problem for the thermoelasticity system. Inverse Problems 27:1, pages 015006.
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Lionel Roques & Michel Cristofol. (2010) On the determination of the nonlinearity from localized measurements in a reaction?diffusion equation. Nonlinearity 23:3, pages 675-686.
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N. Baranibalan, K. Sakthivel, K. Balachandran & J.-H. Kim. (2010) Reconstruction of two time independent coefficients in an inverse problem for a phase field system. Nonlinear Analysis: Theory, Methods & Applications 72:6, pages 2841-2851.
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Assia Benabdallah, Michel Cristofol, Patricia Gaitan & Luz de Teresa. (2010) A new Carleman inequality for parabolic systems with a single observation and applications. Comptes Rendus. Mathématique 348:1-2, pages 25-29.
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Masahiro Yamamoto. (2009) Carleman estimates for parabolic equations and applications. Inverse Problems 25:12, pages 123013.
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