Results 31 to 40 of about 1,641,201 (192)
Lipschitz Stability Estimate and Uniqueness in the Retrospective Analysis for The Mean Field Games System via Two Carleman Estimates [PDF]
, 2023 A retrospective analysis process for the mean field games system (MFGS) is considered. For the first time, Carleman estimates are applied to the analysis of the MFGS. Two new Carleman estimates are derived.
Klibanov, Michael V., Averboukh, Yurii
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A Strongly Ill-Posed Problem for the Equation
Cumhuriyet Science Journal, 2018 In this work, we consider an inverse problem for an elliptic equationwhich is strongly ill-posed in Hadamard sense. We prove the uniqueness of thesolution of the problem by using Carleman estimates.
Mustafa Yıldız
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, 2021 International audienceAbstract For a parabolic equation in the spatial variable x = ( x 1 , … , x n ) {x=(x_{1},\ldots,x_{n})} and time t , we consider an inverse problem of determining a coefficient which is independent of one spatial component x n {x_ ...
Kian, Yavar +8 more
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Insensitizing controls for the Cahn-Hilliard type equation
Electronic Journal of Qualitative Theory of Differential Equations, 2014 This paper is addressed to showing the existence of insensitizing controls for the one-dimensional Cahn--Hilliard type equation with a superlinear nonlinearity. We solve this problem by reducing the original problem to a controllability problem.
Peng Gao
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Uniqueness properties for discrete equations and Carleman estimates
Journal of Functional Analysis, 2017 In the revised version, published in 2017, we improve our Carleman estimate and the method of proof of Theorem 1.1 in order to quantify the uniqueness result in the one dimensional case, proving the sharp uniqueness result conjectured by Lyubarskii, Jaming, Malinnikova and ...
Bertolin, Aingeru Fernández, Vega, Luis
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Approximate controllability of the coupled degenerate system with two boundary controls
Boundary Value Problems, 2017 In this paper, we investigate the approximate controllability of the coupled system with boundary degeneracy. The control functions act on the degenerate boundary. We prove the Carleman estimate and the unique continuation of the adjoint system.
Runmei Du
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Lipschitz stability in an inverse problem for the Korteweg-de Vries equation on a finite domain
Boundary Value Problems, 2017 In this paper, we address an inverse problem for the Korteweg-de Vries equation posed on a bounded domain with boundary conditions proposed by Colin and Ghidaglia.
Mo Chen
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Stabilization of the weakly coupled plate equations with a locally distributed damping
Advances in Difference Equations, 2020 In this paper, we study the indirect stabilization of a system of plate equations which are weakly coupled and locally damped. By virtue of the general results due to Burq in the study of asymptotic behavior of solutions, we prove that the semigroup ...
Xianzheng Zhu
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Carleman’s and subelliptic estimates
Duke Mathematical Journal, 1988 Für einen Differentialoperator P der Ordnung m in \(\Omega \subset R^ n\) und einer glatten reellen Funktion \(\psi\) sei \(P_{\gamma}=e^{-\psi \gamma}Pe^{\psi \gamma}\) mit \(\gamma\geq 1\) gesetzt. Verf. zeigt die Ungleichungen \(\gamma^{1/(k+1)}\| u\|_{m-1,\gamma}\leq C_ K\| P_{\gamma}u\|_{L^ 2}\) und \(\gamma^{-k/(k+1)}\| u\|_{m,\gamma}\leq C_ K ...
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Carleman estimates for stratified media
Journal of Functional Analysis, 2011 Let \(\Omega=\Omega'\times (-H,H)\) be a cylinder in \(\mathbb R^n\), where \(\Omega'\) is a nonempty bounded set in \(\mathbb R^{n-1}\). Let \(S=\Omega'\times\{0\}\) be an interface where coefficients and functions may jump. The authors prove Carleman estimates for anisotropic elliptic and parabolic operators with discontinuities on \(S\).
Benabdallah, Assia +2 more
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