Operator Approach To Linear Problems Of Hydrodynamics Self Adjoint Problems For An Ideal Fluid
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Operator Approach To Linear Problems Of Hydrodynamics Self Adjoint Problems For An Ideal Fluid
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Author : N. D. Kopachevskiĭ
language : en
Publisher: Birkhauser
Release Date : 2001
Operator Approach To Linear Problems Of Hydrodynamics Self Adjoint Problems For An Ideal Fluid written by N. D. Kopachevskiĭ and has been published by Birkhauser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001 with Mathematics categories.
Operator Approach To Linear Problems Of Hydrodynamics
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Author : Nikolay D. Kopachevskii
language : en
Publisher: Springer Science & Business Media
Release Date : 2001-09-01
Operator Approach To Linear Problems Of Hydrodynamics written by Nikolay D. Kopachevskii and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-09-01 with Mathematics categories.
Operator Approach To Linear Problems Of Hydrodynamics
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Author : Nikolay D. Kopachevsky
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06
Operator Approach To Linear Problems Of Hydrodynamics written by Nikolay D. Kopachevsky and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
As mentioned in the Introduction to Volume I, the present monograph is intended both for mathematicians interested in applications of the theory of linear operators and operator-functions to problems of hydrodynamics, and for researchers of applied hydrodynamic problems, who want to study these problems by means of the most recent achievements in operator theory. The second volume considers nonself-adjoint problems describing motions and normal oscillations of a homogeneous viscous incompressible fluid. These ini tial boundary value problems of mathematical physics include, as a rule, derivatives in time of the unknown functions not only in the equation, but in the boundary conditions, too. Therefore, the spectral problems corresponding to such boundary value problems include the spectral parameter in the equation and in the bound ary conditions, and are nonself-adjoint. In their study, we widely used the theory of nonself-adjoint operators acting in a Hilbert space and also the theory of operator pencils. In particular, the methods of operator pencil factorization and methods of operator theory in a space with indefinite metric find here a wide application. We note also that this volume presents both the now classical problems on oscillations of a homogeneous viscous fluid in an open container (in an ordinary state and in weightlessness) and a new set of problems on oscillations of partially dissipative hydrodynamic systems, and problems on oscillations of a visco-elastic or relaxing fluid. Some of these problems need a more careful additional investigation and are rather complicated.
New Difference Schemes For Partial Differential Equations
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Author : Allaberen Ashyralyev
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06
New Difference Schemes For Partial Differential Equations written by Allaberen Ashyralyev and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
The present monograph is devoted to the construction and investigation of the new high order of accuracy difference schemes of approximating the solutions of regular and singular perturbation boundary value problems for partial differential equations. The construction is based on the exact difference scheme and Taylor's decomposition on the two or three points. This approach permitted essentially to extend to a class of problems where the theory of difference methods is applicable. Namely, now it is possible to investigate the differential equations with variable coefficients and regular and singular perturbation boundary value problems. The investigation is based on new coercivity inequalities. The book will be of value to professional mathematicians, as well as advanced students in the fields of numerical analysis, functional analysis, and ordinary and partial differential equations.
The State Space Method
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Author : Daniel Alpay
language : en
Publisher: Springer Science & Business Media
Release Date : 2006
The State Space Method written by Daniel Alpay and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with Language Arts & Disciplines categories.
The state space method developed in the last decades allows us to study the theory of linear systems by using tools from the theory of linear operators; conversely, it had a strong influence on operator theory introducing new questions and topics. The present volume contains a collection of essays representing some of the recent advances in the state space method. Methods covered include noncommutative systems theory, new aspects of the theory of discrete systems, discrete analogs of canonical systems, and new applications to the theory of Bezoutiants and convolution equations. The articles in the volume will be of interest to pure and applied mathematicians, electrical engineers and theoretical physicists.
Recent Advances In Operator Theory And Its Applications
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Author : Israel Gohberg
language : en
Publisher: Springer Science & Business Media
Release Date : 2005-09-16
Recent Advances In Operator Theory And Its Applications written by Israel Gohberg and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-09-16 with Mathematics categories.
This book contains a selection of carefully refereed research papers, most of which were presented at the fourteenth International Workshop on Operator Theory and its Applications (IWOTA), held at Cagliari, Italy, from June 24-27, 2003. The papers, many of which have been written by leading experts in the field, concern a wide variety of topics in modern operator theory and applications, with emphasis on differential operators and numerical methods. The book will be of interest to a wide audience of pure and applied mathematicians and engineers.
Spectral Analysis Of Differential Operators
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Author : Fedor S. Rofe-Beketov
language : en
Publisher: World Scientific
Release Date : 2005
Spectral Analysis Of Differential Operators written by Fedor S. Rofe-Beketov and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Mathematics categories.
This is the first monograph devoted to the Sturm oscillatory theory for infinite systems of differential equations and its relations with the spectral theory. It aims to study a theory of self-adjoint problems for such systems, based on an elegant method of binary relations. Another topic investigated in the book is the behavior of discrete eigenvalues which appear in spectral gaps of the Hill operator and almost periodic SchrAdinger operators due to local perturbations of the potential (e.g., modeling impurities in crystals). The book is based on results that have not been presented in other monographs. The only prerequisites needed to read it are basics of ordinary differential equations and operator theory. It should be accessible to graduate students, though its main topics are of interest to research mathematicians working in functional analysis, differential equations and mathematical physics, as well as to physicists interested in spectral theory of differential operators."
Nonlinear Dynamics
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Author : Ivan A. Lukovsky
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2015-04-24
Nonlinear Dynamics written by Ivan A. Lukovsky and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-04-24 with Mathematics categories.
This book is devoted to analytically approximate methods in the nonlinear dynamics of a rigid body with cavities (containers) partly filled by a liquid. The methods are normally based on the Bateman-Luke variational formalism combined with perturbation theory. The derived approximate equations of spatial motions of the body-liquid mechanical system (these equations are called mathematical models in the title) take the form of a finite-dimensional system of nonlinear ordinary differential equations coupling quasi-velocities of the rigid body motions and generalized coordinates responsible for displacements of the natural sloshing modes. Algorithms for computing the hydrodynamic coefficients in the approximate mathematical models are proposed. Numerical values of these coefficients are listed for some tank shapes and liquid fillings. The mathematical models are also derived for the contained liquid characterized by the Newton-type dissipation. Formulas for hydrodynamic force and moment are derived in terms of the solid body quasi-velocities and the sloshing-related generalized coordinates. For prescribed harmonic excitations of upright circular (annular) cylindrical and/or conical tanks, the steady-state sloshing regimes are theoretically classified; the results are compared with known experimental data. The book can be useful for both experienced and early-stage mechanicians, applied mathematicians and engineers interested in (semi-)analytical approaches to the “fluid-structure” interaction problems, their fundamental mathematical background as well as in modeling the dynamics of complex mechanical systems containing a rigid tank partly filled by a liquid.
Sloshing In Upright Circular Containers
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Author : Ihor Raynovskyy
language : en
Publisher: CRC Press
Release Date : 2020-10-08
Sloshing In Upright Circular Containers written by Ihor Raynovskyy and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-10-08 with Technology & Engineering categories.
This book presents mathematical fundaments and results on sloshing in an upright circular cylindrical tank with semi-analytical solutions. The book outlines generic mathematical and physical aspects of the multimodal method, describes milestones, and presents several versions of modal systems for an upright circular tank, both linear and nonlinear. The book offers an extended description of the state-of-the-art theoretical sloshing with more than 200 references. It presents mathematical fundamentals of free-surface sloshing problems, details linear and nonlinear modal equations, provides analytical estimates of viscous damping, and covers stability analysis of steady-state solution. The book is for engineers dealing with sloshing, applied mathematicians working on free-surface problems, and lecturers in fluid mechanics that need to know the fundamentals and analytical solutions from surface wave theory.
Differential Equations Mathematical Physics And Applications Selim Grigorievich Krein Centennial
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Author : Peter Kuchment
language : en
Publisher: American Mathematical Soc.
Release Date : 2019-07-22
Differential Equations Mathematical Physics And Applications Selim Grigorievich Krein Centennial written by Peter Kuchment and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-07-22 with Mathematics categories.
This is the second of two volumes dedicated to the centennial of the distinguished mathematician Selim Grigorievich Krein. The companion volume is Contemporary Mathematics, Volume 733. Krein was a major contributor to functional analysis, operator theory, partial differential equations, fluid dynamics, and other areas, and the author of several influential monographs in these areas. He was a prolific teacher, graduating 83 Ph.D. students. Krein also created and ran, for many years, the annual Voronezh Winter Mathematical Schools, which significantly influenced mathematical life in the former Soviet Union. The articles contained in this volume are written by prominent mathematicians, former students and colleagues of Selim Krein, as well as lecturers and participants of Voronezh Winter Schools. They are devoted to a variety of contemporary problems in ordinary and partial differential equations, fluid dynamics, and various applications.