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Author: Martin Wechselberger
Publisher: Springer Nature
ISBN: 3030363996
Category : Mathematics
Languages : en
Pages : 143
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Book Description
This volume provides a comprehensive review of multiple-scale dynamical systems. Mathematical models of such multiple-scale systems are considered singular perturbation problems, and this volume focuses on the geometric approach known as Geometric Singular Perturbation Theory (GSPT). It is the first of its kind that introduces the GSPT in a coordinate-independent manner. This is motivated by specific examples of biochemical reaction networks, electronic circuit and mechanic oscillator models and advection-reaction-diffusion models, all with an inherent non-uniform scale splitting, which identifies these examples as singular perturbation problems beyond the standard form. The contents cover a general framework for this GSPT beyond the standard form including canard theory, concrete applications, and instructive qualitative models. It contains many illustrations and key pointers to the existing literature. The target audience are senior undergraduates, graduate students and researchers interested in using the GSPT toolbox in nonlinear science, either from a theoretical or an application point of view. Martin Wechselberger is Professor at the School of Mathematics & Statistics, University of Sydney, Australia. He received the J.D. Crawford Prize in 2017 by the Society for Industrial and Applied Mathematics (SIAM) for achievements in the field of dynamical systems with multiple time-scales.
Author: Martin Wechselberger
Publisher: Springer Nature
ISBN: 3030363996
Category : Mathematics
Languages : en
Pages : 143
Get Book Here
Book Description
This volume provides a comprehensive review of multiple-scale dynamical systems. Mathematical models of such multiple-scale systems are considered singular perturbation problems, and this volume focuses on the geometric approach known as Geometric Singular Perturbation Theory (GSPT). It is the first of its kind that introduces the GSPT in a coordinate-independent manner. This is motivated by specific examples of biochemical reaction networks, electronic circuit and mechanic oscillator models and advection-reaction-diffusion models, all with an inherent non-uniform scale splitting, which identifies these examples as singular perturbation problems beyond the standard form. The contents cover a general framework for this GSPT beyond the standard form including canard theory, concrete applications, and instructive qualitative models. It contains many illustrations and key pointers to the existing literature. The target audience are senior undergraduates, graduate students and researchers interested in using the GSPT toolbox in nonlinear science, either from a theoretical or an application point of view. Martin Wechselberger is Professor at the School of Mathematics & Statistics, University of Sydney, Australia. He received the J.D. Crawford Prize in 2017 by the Society for Industrial and Applied Mathematics (SIAM) for achievements in the field of dynamical systems with multiple time-scales.
Author: Sergio Albeverio
Publisher: Cambridge University Press
ISBN: 9780521779128
Category : Mathematics
Languages : en
Pages : 454
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Book Description
This is a systematic mathematical study of differential (and more general self-adjoint) operators.
Author: Pavel Kurasov
Publisher: Springer Nature
ISBN: 3030315312
Category : Mathematics
Languages : en
Pages : 635
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Book Description
Boris Pavlov (1936-2016), to whom this volume is dedicated, was a prominent specialist in analysis, operator theory, and mathematical physics. As one of the most influential members of the St. Petersburg Mathematical School, he was one of the founders of the Leningrad School of Non-self-adjoint Operators. This volume collects research papers originating from two conferences that were organized in memory of Boris Pavlov: “Spectral Theory and Applications”, held in Stockholm, Sweden, in March 2016, and “Operator Theory, Analysis and Mathematical Physics – OTAMP2016” held at the Euler Institute in St. Petersburg, Russia, in August 2016. The volume also includes water-color paintings by Boris Pavlov, some personal photographs, as well as tributes from friends and colleagues.
Author: Tosio Kato
Publisher: Springer Science & Business Media
ISBN: 3662126788
Category : Mathematics
Languages : en
Pages : 610
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Book Description
Author: Olivier Alvarez
Publisher: American Mathematical Soc.
ISBN: 0821867016
Category : Mathematics
Languages : en
Pages : 90
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Book Description
"Volume 204, number 960 (fourth of 5 numbers)."
Author: Petar Kokotovic
Publisher: SIAM
ISBN: 9781611971118
Category : Mathematics
Languages : en
Pages : 386
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Book Description
Singular perturbations and time-scale techniques were introduced to control engineering in the late 1960s and have since become common tools for the modeling, analysis, and design of control systems. In this SIAM Classics edition of the 1986 book, the original text is reprinted in its entirety (along with a new preface), providing once again the theoretical foundation for representative control applications. This book continues to be essential in many ways. It lays down the foundation of singular perturbation theory for linear and nonlinear systems, it presents the methodology in a pedagogical way that is not available anywhere else, and it illustrates the theory with many solved examples, including various physical examples and applications. So while new developments may go beyond the topics covered in this book, they are still based on the methodology described here, which continues to be their common starting point.
Author: Jan Janas
Publisher: Springer Science & Business Media
ISBN: 3764381353
Category : Mathematics
Languages : en
Pages : 261
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Book Description
This volume contains lectures delivered at the International Conference Operator Theory and its Applications in Mathematical Physics (OTAMP 2004), held at the Mathematical Research and Conference Center in Bedlewo near Poznan, Poland. The idea behind these lectures was to present interesting ramifications of operator methods in current research of mathematical physics.
Author: Adelaida B. Vasil'eva
Publisher: SIAM
ISBN: 0898713331
Category : Mathematics
Languages : en
Pages : 231
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Book Description
This book is devoted solely to the boundary function method, which is one of the asymptotic methods.
Author: Sergio Albeverio
Publisher:
ISBN: 9781107089419
Category : MATHEMATICS
Languages : en
Pages : 446
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Book Description
This is a systematic mathematical study of differential (and more general self-adjoint) operators.
Author: Fedor S. Rofe-Beketov
Publisher: World Scientific
ISBN: 9812703454
Category : Mathematics
Languages : en
Pages : 466
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Book Description
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."
