Gromov-Hausdorff Stability of Dynamical Systems and Applications to PDEs, Lee

Автор: Gromov
Название: Partial differential relations
ISBN: 3540121773 ISBN-13(EAN): 9783540121770
Издательство: Springer
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Цена: 16769.00 р.
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Описание: The classical theory of partial differential equations is rooted in physics, where equations (are assumed to) describe the laws of nature. We deal in this book with a completely different class of partial differential equations (and more general relations) which arise in differential geometry rather than in physics.

Автор: Yingjie Liang, Wen Chen, Wei Cai
Название: Hausdorff Calculus: Applications to Fractal Systems
ISBN: 3110606925 ISBN-13(EAN): 9783110606928
Издательство: Walter de Gruyter
Цена: 22305.00 р.
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Описание: The series is devoted to the publication of high-level monographs which cover progresses in fractional calculus research in mathematics and applications in physics, mechanics, engineering and biology etc. Methodological aspects e.g., theory, modeling and computational methods are presented from mathematical point of view, and emphases are placed in computer simulation, analysis, design and control of application-oriented issues in various scientific disciplines. It is designed for mathematicians, and researchers using fractional calculus as a tool in the field of physics, mechanics, engineering and biology. Contributions which are interdisciplinary and which stimulate further research at the crossroads of sciences and engineering are particularly welcomed. Editor-in-chief: Changpin Li, Shanghai University, China Editorial Board: Virginia Kiryakova, Bulgarian Academy of Sciences, Bulgaria Francesco Mainardi, University of Bologna, Italy Dragan Spasic, University of Novi Sad, Serbia Bruce Ian Henry, University of New South Wales, Australia YangQuan Chen, University of California, Merced, USA Please submit book proposals to Professor Changpin Li: lcp@shu.edu.cn

Автор: Bl. Sendov; Gerald Beer
Название: Hausdorff Approximations
ISBN: 9401067872 ISBN-13(EAN): 9789401067874
Издательство: Springer
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Цена: 15372.00 р.
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Описание: 'Et moi, ..., si j'avait su comment en revenir, One service mathematics has rendered the je n'y serais point a1Ie.' human race. It has put common sense back Jules Verne where it belongs, on the topmost shelf next to the dusty canister labelled 'discarded non- The series is divergent; therefore we may be sense'. able to do something with it. Eric T. Bell O. Heaviside Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and non- linearities abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics .. .'; 'One service logic has rendered com- puter science .. .'; 'One service category theory has rendered mathematics .. .'. All arguably true. And all statements obtainable this way form part of the raison d'etre of this series.

Автор: Gromov, Mikhail
Название: Metric structures for riemannian and non-riemannian spaces
ISBN: 0817645829 ISBN-13(EAN): 9780817645823
Издательство: Springer
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Цена: 15372.00 р.
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Описание: This book is an English translation of the famous "Green Book" by Lafontaine and Pansu (1979).

Автор: Iasson Karafyllis; Miroslav Krstic
Название: Input-to-State Stability for PDEs
ISBN: 3030081559 ISBN-13(EAN): 9783030081553
Издательство: Springer
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Цена: 20962.00 р.
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Описание: This book lays the foundation for the study of input-to-state stability (ISS) of partial differential equations (PDEs) predominantly of two classes—parabolic and hyperbolic. This foundation consists of new PDE-specific tools. In addition to developing ISS theorems, equipped with gain estimates with respect to external disturbances, the authors develop small-gain stability theorems for systems involving PDEs. A variety of system combinations are considered: PDEs (of either class) with static maps;PDEs (again, of either class) with ODEs;PDEs of the same class (parabolic with parabolic and hyperbolic with hyperbolic); andfeedback loops of PDEs of different classes (parabolic with hyperbolic).In addition to stability results (including ISS), the text develops existence and uniqueness theory for all systems that are considered. Many of these results answer for the first time the existence and uniqueness problems for many problems that have dominated the PDE control literature of the last two decades, including—for PDEs that include non-local terms—backstepping control designs which result in non-local boundary conditions.Input-to-State Stability for PDEs will interest applied mathematicians and control specialists researching PDEs either as graduate students or full-time academics. It also contains a large number of applications that are at the core of many scientific disciplines and so will be of importance for researchers in physics, engineering, biology, social systems and others.