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Applications of Observability Inequalities
SEMA SIMAI Springer Series, 2019This article presents two observability inequalities for the heat equation over Ω × (0, T). In the first one, the observation is from a subset of positive measure in Ω × (0, T), while in the second, the observation is from a subset of positive surface measure on ∂Ω × (0, T).
Jone Apraiz
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SIAM Journal on Control and Optimization, 2016 This paper aims to provide directly the observability inequality of backward stochastic heat equations for measurable sets. As an immediate application, the null controllability of the forward heat equations is obtained.
Jie Zhong, Donghui Yang
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Observability Inequalities by Internal Observation and Their Applications
Journal of Optimization Theory and Applications, 2003The systems under study are described by the wave equation \[ {\partial^2 y(t, x) \over \partial t^2} - \Delta y(t, x) = a_1(t, x)y(t, x) + a_2(t, x) {\partial y(t, x) \over \partial t} + \langle a_3(t, x), \nabla y(t, x) \rangle \] in a \(n\)-dimensional domain \(\Omega\) with boundary \(\Gamma,\) with initial conditions \[ y(0, x) = y_0(x),\;\partial
Liu, K., Yamamoto, M., Zhang, X.
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Observability Inequalities on Measurable Sets for the Stokes System and Applications [PDF]
SIAM Journal on Control and Optimization, 2020 In this paper, we establish spectral inequalities on measurable sets of positive Lebesgue measure for the Stokes operator, as well as an observability inequalities on space-time measurable sets of positive measure for non-stationary Stokes system. Furthermore, we provide their applications in the theory of shape optimization and time optimal control ...
Diego A. Souza, Felipe W. Chaves-Silva
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Observations on Moser's inequality
Archive for Rational Mechanics and Analysis, 1989Starting from the limiting case of the Sobolev imbedding theorem of Trudinger, Moser has proved two different one-dimensional inequalities of more general nature. One of them has its applications in partial differential equations, the other in differential geometry.
McLeod, J. B., Peletier, L. A.
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2019
This chapter advocates the development of comparative organizational research designs as the empirical basis for studying both the generic and contingent processes that generate inequality. After explaining where past quantitative and qualitative researchers have gone wrong, it goes on to examine and promote contemporary comparative organizational ...
Donald Tomaskovic-Devey +1 more
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This chapter advocates the development of comparative organizational research designs as the empirical basis for studying both the generic and contingent processes that generate inequality. After explaining where past quantitative and qualitative researchers have gone wrong, it goes on to examine and promote contemporary comparative organizational ...
Donald Tomaskovic-Devey +1 more
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Bell’s Inequality for Trichotomic Observables
1995In order to give a more complete description of an actual experiment on EPR paradox, the upper limits for Bell and Clauser-Horn-Shimony-Holt inequalities are deduced in the case of three-valued observables. This limit results a function of the supplementary assumptions.
Garuccio A, De Caro L
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Observability in linear systems of equations and inequalities: Applications
Computers and Operations Research, 2007zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Antonio J Conejo +2 more
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Bell’s inequality, trichotomic observables, and supplementary assumptions
Physical Review A, 1996A general approach to Bell-type inequalities for trichotomic observables is presented. With this formalism, which explicitly includes no-counts events, we show that the limits of all Bell-type inequalities are functions of the supplementary assumptions.
De Caro L, Garuccio A
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Observability Inequality at Two Time Points for KdV Equations
SIAM Journal on Mathematical Analysis, 2021The aim of this paper is to prove an observability inequality from two time points for the linear Korteweg-de Vries (KdV) equation with an explicit constant. The proof relies on a quantitative analytic estimate for the linear KdV with compact support initial data and an uncertainty principle of super-analytic functions.
Ze Li, Ming Wang 0003
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