Results 121 to 130 of about 161 (155)

Carleman Estimates for Second-Order Hyperbolic Equations

Siberian Mathematical Journal, 2006
Summary: 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

2004
In 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 Some Thermoelasticity Systems

2017
In this chapter, we establish Carleman estimates for a thermoelastic plate system and a thermoelastic system with residual stress as applications of the Carleman estimate in Chap. 4.
Bellassoued M., Yamamoto M.
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Carleman estimates for parabolic equations and applications

Inverse Problems, 2009
In 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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GLOBAL CARLEMAN ESTIMATES FOR DEGENERATE PARABOLIC OPERATORS WITH APPLICATIONS

Memoirs of the American Mathematical Society, 2015
Degenerate parabolic operators have received increasing attention in recent years because they are associated with both important theoretical analysis, such as stochastic diffusion processes, and interesting applications to engineering, physics, biology, and economics.
Cannarsa, Piermarco, Martinez, Patrick, Vancostenoble, Judith   +2 more
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Carleman Estimates and Applications to Inverse Problems

Milan Journal of Mathematics, 2004
Click 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 differential equations.
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Carleman estimates for second-order hyperbolic systems in anisotropic cases and applications. Part I: Carleman estimates

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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Inverse Problems and Carleman Estimates

2021
Michael V. Klibanov, Jingzhi Li
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Optimality Aspects of Carleman Estimates

2021
Jérôme Le Rousseau, Gilles Lebeau, Luc Robbiano   +2 more
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Carleman Estimates via Brenner’s Theorem and Strichartz Estimates

2019
In this chapter, we study more systematically \(L^{p}-L^{q}\) Carleman estimates, mainly following the articles of C. Sogge ([141]), D. Tataru ([153]), H. Koch and D. Tataru [83] and D. Dos Santos Ferreira ([34, 35]). In contrast to \(L^{2}-L^{2}\) estimates, where Hilbertian methods and integration by parts can be used, the \(L^{p}-L^{q}\) Carleman ...
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