Results 21 to 30 of about 4,144 (169)
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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Determining nonsmooth first order terms from partial boundary measurements [PDF]
, 2006 We extend results of Dos Santos Ferreira-Kenig-Sjoestrand-Uhlmann (math.AP/0601466) to less smooth coefficients, and we show that measurements on part of the boundary for the magnetic Schroedinger operator determine uniquely the magnetic field related to
Knudsen, Kim, Salo, Mikko
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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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Inverse Problems for Parabolic Equation with Discontinuous Coefficients
Nonautonomous Dynamical Systems, 2017 We consider the reaction-diffusion equation with discontinuities in the diffusion coefficient and the potential term. We start by deriving the Carleman estimate for the discontinuous reaction-diffusion operator which is deployed in the inverse problems ...
Dinakar V. +2 more
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Carleman estimate for the Navier–Stokes equations and applications [PDF]
Inverse Problems, 2022 Abstract For linearized Navier–Stokes equations, we first derive a Carleman estimate with a regular weight function. Then we apply it to establish conditional stability for the lateral Cauchy problem and finally we prove conditional stability estimates for the inverse source problem of determining a spatially varying divergence-free ...
Oleg Y Imanuvilov +2 more
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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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Uniqueness properties for discrete equations and Carleman estimates
Journal of Functional Analysis, 2017 Using Carleman estimates, we give a lower bound for solutions to the discrete Schr dinger equation in both dynamic and stationary settings that allows us to prove uniqueness results, under some assumptions on the decay of the solutions.
Bertolin, Aingeru Fernández, Vega, Luis
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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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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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, 2017 In this paper we prove a H\"older propagation of smallness for solutions to second order parabolic equations whose general anisotropic leading coefficient has a jump at an interface.
Francini, Elisa, Vessella, Sergio
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