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2017
In this monograph, we discuss the derivation of Carleman estimates and their application to inverse problems of determining spatially varying coefficients or source terms. The inverse problem is to determine unknown quantities in governing equations from available data of solutions.
Bellassoued M., Yamamoto M.
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In this monograph, we discuss the derivation of Carleman estimates and their application to inverse problems of determining spatially varying coefficients or source terms. The inverse problem is to determine unknown quantities in governing equations from available data of solutions.
Bellassoued M., Yamamoto M.
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Carleman Estimates of Refined Stochastic Beam Equations and Applications
SIAM Journal on Control and Optimization, 2022This paper is devoted to establishing global Carleman estimates for refined stochastic beam equations. First, by establishing a fundamental weighted identity, two Carleman estimates are derived with different weight functions for the refined stochastic beam equation, which is a coupled system consisting of a stochastic ordinary differential equation ...
Yongyi Yu, Ji-Feng Zhang
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Carleman Estimate for a Hyperbolic-Parabolic System
Differential Equations, 2019zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Inverse problems and Carleman estimates
Inverse Problems, 1992The author describes the current state of the method of Carleman type estimates suggested by \textit{A. L. Bukhgejm} and himself [Dokl. Akad. Nauk SSSR 260, 269-272 (1981; Zbl 0497.35082)]. This method is based on powerful estimates of solutions of PDE in weighted Sobolev spaces which are a classical tool in the uniqueness of continuation study as well
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Carleman Estimates and Controllability of Linear Stochastic Heat Equations
Applied Mathematics and Optimization, 2003zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Barbu, V +2 more
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Carleman Estimates for Second-Order Hyperbolic Equations
Siberian Mathematical Journal, 2006Summary: In the space of variables \((x,t)\in\mathbb R^{n+1}\), we consider a linear second-order hyperbolic equation with coefficients depending only on \(x\). Given a domain \(D\subset\mathbb R^{n+1}\) whose projection to the \(x\)-space is a compact domain \(\Omega\), we consider the question of construction of a stability estimate for a solution to
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Carleman Type Estimates and Their Applications
2004In these lecture notes we derive Carleman type estimates for second order linear partial differential operators and show some of their applications to the uniqueness in the Cauchy problem, approximate and exact controllability, and inverse problems. In section 2 we discuss pseudo-convexity and derive Carleman type estimates with boundary terms.
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Carleman estimates for parabolic equations and applications
Inverse Problems, 2009In this review, concerning parabolic equations, we give self-contained descriptions on derivations of Carleman estimates; methods for applications of the Carleman estimates to estimates of solutions and to inverse problems.Moreover limited to parabolic equations, we survey the previous and recent results in view of the applicability of the Carleman ...
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Carleman Estimates and Applications to Inverse Problems
Milan Journal of Mathematics, 2004Click on the DOI link to access the article (may not be free) ; This review paper describes some general and recent results of possible interest for mathematicians studying or using uniqueness of the continuation or working on control theory or inverse problems for partial diļ¬erential equations.
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Applicable Analysis, 2014
In this paper, we consider Carleman-type estimates and an inverse source problem for second-order hyperbolic systems in an anisotropic case. In Part I, we establish a Carleman-type estimate for hyperbolic systems in an anisotropic case by assuming that the coefficient matrices in the systems satisfy suitable conditions and taking the weight function ...
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In this paper, we consider Carleman-type estimates and an inverse source problem for second-order hyperbolic systems in an anisotropic case. In Part I, we establish a Carleman-type estimate for hyperbolic systems in an anisotropic case by assuming that the coefficient matrices in the systems satisfy suitable conditions and taking the weight function ...
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