Estimating anisotropic norm of system with linear-fractional uncertainty

2016 ◽  
Author(s):  
Michael M. Tchaikovsky
Keyword(s):  
Anisotropic Norm ◽  
Linear Fractional Uncertainty

Strict Anisotropic Norm Bounded Real Lemma in Terms of Inequalities

2011 ◽  
Vol 44 (1) ◽  
pp. 2332-2337 ◽  
Author(s):  
Michael M. Tchaikovsky ◽  
Alexander P. Kurdyukov ◽  
Victor N. Timin
Keyword(s):  
Bounded Real Lemma ◽  
Anisotropic Norm

scholarly journals On Computing the Anisotropic Norm of Linear Discrete-Time-Invariant Systems

1996 ◽  
Vol 29 (1) ◽  
pp. 3057-3062 ◽  
Author(s):  
I.G. Vladimirov ◽  
A.P. Kurdjukov ◽  
A.V. Semyonov
Keyword(s):  
Discrete Time ◽  
Anisotropic Norm ◽  
Time Invariant

scholarly journals Perturbative Cauchy theory for a flux-incompressible Maxwell-Stefan system

2022 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Andrea Bondesan ◽  
Marc Briant
Keyword(s):  
Equilibrium State ◽  
Existence And Uniqueness ◽  
Quasilinear Parabolic Equation ◽  
Strong Solutions ◽  
Cross Diffusion ◽  
Anisotropic Norm ◽  
Exponential Trend ◽  
Perturbative Regime ◽  
Global Existence And Uniqueness ◽  
Quasilinear Parabolic

<p style='text-indent:20px;'>Recently, the authors proved [<xref ref-type="bibr" rid="b2">2</xref>] that the Maxwell-Stefan system with an incompressibility-like condition on the total flux can be rigorously derived from the multi-species Boltzmann equation. Similar cross-diffusion models have been widely investigated, but the particular case of a perturbative incompressible setting around a non constant equilibrium state of the mixture (needed in [<xref ref-type="bibr" rid="b2">2</xref>]) seems absent of the literature. We thus establish a quantitative perturbative Cauchy theory in Sobolev spaces for it. More precisely, by reducing the analysis of the Maxwell-Stefan system to the study of a quasilinear parabolic equation on the sole concentrations and with the use of a suitable anisotropic norm, we prove global existence and uniqueness of strong solutions and their exponential trend to equilibrium in a perturbative regime around any macroscopic equilibrium state of the mixture. As a by-product, we show that the equimolar diffusion condition naturally appears from this perturbative incompressible setting.</p>

scholarly journals The Anisotropic Norm of Signals: Towards Possible Definitions

2018 ◽  
Vol 51 (32) ◽  
pp. 169-174
Author(s):  
K.R. Chernyshov
Keyword(s):  
Anisotropic Norm
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