Essential Spectra of a 3 × 3 Operator Matrix and an Application to Three-Group Transport Equations

Amar, Afif Ben; Jeribi, Aref; Krichen, Bilel

doi:10.1007/s00020-010-1798-3

Cited by 27 publications

(4 citation statements)

References 26 publications

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“…3 (µ) and M 31 are in F (X), then σ e 4 ,M 22 (S 2 (µ)) and σ e 5 ,M 22 (S 2 (µ)) do not depend on µ.Proof. (i) Follows immediately from the equation(5). (ii) Let λ, µ ∈ ρ M 11 (A) ∩ ρ M 22 (S 1 (µ)).…”

mentioning

confidence: 95%

“…Similarly, [15] study the M-essential spectra of 2 × 2 operator matrix. Whereas in the paper of [5], Aref and all investigate the essential spectra of a 3 × 3 blok operator matrix.…”

Section: Introductionmentioning

confidence: 99%

“…The purpose of this work is to pursue the analysis started in [4,5,8,15,19]. In Section 1, we establish some stability results on Fredholm theory.…”

Section: Introductionmentioning

confidence: 99%

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Perturbation theory, M-essential spectra of operator matrices

Abdelmoumen

Yengui

2020

Filomat

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mentioning

confidence: 95%

“…Similarly, [15] study the M-essential spectra of 2 × 2 operator matrix. Whereas in the paper of [5], Aref and all investigate the essential spectra of a 3 × 3 blok operator matrix.…”

Section: Introductionmentioning

confidence: 99%

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Perturbation theory, M-essential spectra of operator matrices

Abdelmoumen

Yengui

2020

Filomat

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“…For many applications this is sufficient, and some larger block operator matrices can treated iteratively by different 2 × 2-block decompositions. However, also larger block structures such as 3 × 3-or general n × n-block operator matrices have been studied as well, see [13] and also [105,Section 1.11], respectively. Spectral problems for block operator matrices and corresponding forms are discussed also in [35,36,[62][63][64]78,92,95], see also the references therein.…”

Section: Introductionmentioning

confidence: 99%

Maximal $L^p$-regularity and $H^{\infty}$-calculus for block operator matrices and applications

Agresti¹,

Hussein²

2021

Preprint

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Many coupled evolution equations can be described via 2×2-block operator matrices of the formwith possibly unbounded entries. Here, the case of diagonally dominant block operator matrices is considered, that is, the case where the full operator A can be seen as a relatively bounded perturbation of its diagonal part with D(A) = D(A) × D(D) though with possibly large relative bound. For such operators the properties of sectoriality, R-sectoriality and the boundedness of the H ∞ -calculus are studied, and for these properties perturbation results for possibly large but structured perturbations are derived. Thereby, the time dependent parabolic problem associated with A can be analyzed in maximal L p t -regularity spaces, and this is applied to a wide range of problems such as different theories for liquid crystals, an artificial Stokes system, strongly damped wave and plate equations, and a Keller-Segel model.

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Introduction

Jeribi¹

2015

Spectral Theory and Applications of Linear Operators and Block Operator Matrices

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IntroductionThis book is devoted to some recent mathematical developments which cover several topics including Cauchy problem, Fredholm operators, spectral theory, and block operator matrices, both dealing with linear operators. Of course, these topics play a crucial role in many branches of mathematics and also in numerous applications as they are intimately related to the stability of the underlying physical systems.One of the objectives of this book is the study of the classical Riesz theory of polynomially compact operators, in order to establish the existence results of the second kind operator equations, hence allowing to describe the spectrum, multiplicities, and localization of the eigenvalues of polynomially compact operators. Fredholm theory and perturbation results are also widely investigated. The description of the large time behavior of solutions to an abstract Cauchy problem on Banach spaces without restriction on the initial data is studied. Further, the essential state of the art of research and essential pseudo-spectra of closed, densely defined, and linear operators subjected to additive perturbations is outlined. The spectral theory of block operator matrices is of major interest, since it describes coupled systems of partial differential equations of mixed order and type. For this reason, an important part of this book is devoted to develop essential spectra of 2 2 and 3 3 block operator matrices. Based on the spectral graph theory (which is an active research area), we are interested in the study of the adjacency matrix and the discrete Laplacian acting on forms. Most of the results of this book are motivated by physical transport problems for which we address our applications at the end of the book. Now, let us describe its contents.

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Essential Spectra of a 3 × 3 Operator Matrix and an Application to Three-Group Transport Equations

Cited by 27 publications

References 26 publications

Perturbation theory, M-essential spectra of operator matrices

Perturbation theory, M-essential spectra of operator matrices

Maximal $L^p$-regularity and $H^{\infty}$-calculus for block operator matrices and applications

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