Results 21 to 30 of about 161 (155)
On non-quasianalytic classes of infinitely differentiable functions
Учёные записки Казанского университета: Серия Физико-математические науки, 2022 This article investigates the connection between two positive logarithmically convex sequences {M̂n} and {Mn}, which define respectively the Carleman classes of functions infinitely differentiable on the set J and sequences {bn} specifying the values of ...
G.S. Balashova
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Controllability results for weakly blowing up reaction-diffusion system
Electronic Journal of Qualitative Theory of Differential Equations, 2012 In this paper, we consider the controllability of a general reaction-diffusion system with homogeneous Dirichlet boundary conditions. We prove the exact controllability to the trajectories and the approximate controllability of the system which contains ...
Qiang Tao, Hang Gao, Ying Yang
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A strongly ill-posed integro-differential parabolic problem with integral boundary conditions
Mathematical Modelling and Analysis, 2013 Via Carleman estimates we prove uniqueness and continuous dependence results for an identification and strongly ill-posed linear integro-differential parabolic problem with the Dirichlet boundary condition, but with no initial condition.
Alfredo Lorenzi
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Carleman inequality for a class of super strong degenerate parabolic operators and applications
Electronic Journal of Qualitative Theory of Differential Equations, 2023 In this paper, we present a new Carleman estimate for the adjoint equations associated to a class of super strong degenerate parabolic linear problems. Our approach considers a standard geometric imposition on the control domain, which can not be removed
Bruno Sérgio Araújo +2 more
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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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Null controllability of a nonlinear heat equation
Abstract and Applied Analysis, 2002 We study the internal exact null controllability of a nonlinear heat equation with homogeneous Dirichlet boundary condition. The method used combines the Kakutani fixed-point theorem and the Carleman estimates for the backward adjoint linearized system ...
G. Aniculăesei, S. Aniţa
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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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On controllability of waves and geometric Carleman estimates
Séminaire Laurent Schwartz — EDP et applications, 2019 The present article is a brief summary of the paper [27], which established new Carleman and observability estimates for a general class of linear wave equations. The main features of these estimates are that (a) they apply to a fully general class of time-dependent domains , with
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Carleman Estimates with a Second Large Parameter
Journal of Mathematical Analysis and Applications, 2000 Unique continuation of solutions to linear partial differential equations is of importance in many branches of applied mathematics, in particular, in control theory and inverse problems. The Carleman estimates are an important tool for proving the unique continuation for linear operators with non-analytic coefficients.
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