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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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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 via Brenner’s Theorem and Strichartz Estimates
2019In 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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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 differential equations.
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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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Estimation of Carleman operator from a univariate time series
Chaos: An Interdisciplinary Journal of Nonlinear ScienceReconstructing a nonlinear dynamical system from empirical time series is a fundamental task in data-driven analysis. One of the main challenges is the existence of hidden variables; we only have records for some variables, and those for hidden variables are unavailable.
Sherehe Semba +4 more
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