Results 11 to 20 of about 19,539 (276)
Carleman estimates for the one-dimensional heat equation with a discontinuous coefficient and applications [PDF]
, 2006 International audienceWe study the observability and some of its consequences for the one-dimensional heat equation with a discontinuous coefficient (piecewise $\Con^1$).
Benabdallah, Assia +2 more
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Observability and uniqueness theorem for a coupled hyperbolic system
International Journal of Mathematics and Mathematical Sciences, 2000 We deal with the inverse inequality for a coupled hyperbolic system with dissipation. The inverse inequality is an indispensable inequality that appears in the Hilbert Uniqueness Method (HUM), to establish equivalence of norms which guarantees uniqueness
Boris V. Kapitonov, Joel S. Souza
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Geometric control condition for the wave equation with a time-dependent observation domain [PDF]
, 2016 We characterize the observability property (and, by duality, the controllability and the stabilization) of the wave equation on a Riemannian manifold $\Omega,$ with or without boundary, where the observation (or control) domain is time-varying.
Lebeau, Gilles +3 more
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Unique continuation estimates for the Kolmogorov equation in the whole space [PDF]
, 2015 We prove in this Note an observation estimate at one point in time for the Kolmogorov equation in the whole space. Such estimate implies the observability and the null controllability for the Kolmogorov equation with a control region which is ...
Zhang, Yubiao
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Fault Location Observability using Phasor Measurements Units via Semidefinite Programming
IEEE Access, 2016 This paper presents a placement algorithm for fault location observability using phasor measurement units (PMUs) in the presence or absence of zero injection buses.
Theodoros A. Alexopoulos +2 more
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Observed inequality in urban greenspace exposure in China
Environment International, 2021 Given the important role of green environments playing in healthy cities, the inequality in urban greenspace exposure has aroused growing attentions. However, few comparative studies are available to quantify this phenomenon for cities with different population sizes across a country, especially for those in the developing world. Besides, commonly used
Yimeng Song +13 more
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Sharp Observability Inequalities for Hyperbolic Systems with Potentials
ESAIM: Control, Optimisation and Calculus of Variations, 2023 This paper is devoted to a sharp internal/boundary observability inequality for a hyperbolic system with a zero order potential. For this purpose, we first establish a new Carleman estimate for hyperbolic operator inH1-norm. Based on this Carleman estimate and a modified auxiliary optimal control problem, we obtain Carleman estimate for hyperbolic ...
Fu, Xiaoyu, Liao, Zhonghua, Lü, Qi
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Asymptotics for optimal design problems for the Schr\"odinger equation with a potential [PDF]
, 2018 We study the problem of optimal observability and prove time asymptotic observability estimates for the Schr\"odinger equation with a potential in $L^{\infty}(\Omega)$, with $\Omega\subset \mathbb{R}^d$, using spectral theory. An elegant way to model the
Merkurjev, Ekaterina, Waters, Alden
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Electronic Journal of Qualitative Theory of Differential Equations, 2018 We deal with a control problem for a coupled system of two degenerate singular parabolic equations in non-divergence form with degeneracy and singularity appearing at an interior point of the space domain. In particular, we consider the well-posedness of
Jawad Salhi
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Optimal Placement of Phasor Measurement Unit in Smart Grids Considering Multiple Constraints
Journal of Modern Power Systems and Clean Energy, 2023 The distribution of measurement noise is usually assumed to be Gaussian in the optimal phasor measurement unit (PMU) placement (OPP) problem. However, this is not always accurate in practice.
Tengpeng Chen +4 more
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