Asymptotic Methods For Investigating Quasiwave Equations Of Hyperbolic Type
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Asymptotic Methods For Investigating Quasiwave Equations Of Hyperbolic Type
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Author : Yuri A. Mitropolsky
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Asymptotic Methods For Investigating Quasiwave Equations Of Hyperbolic Type written by Yuri A. Mitropolsky 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 2012-12-06 with Mathematics categories.
The theory of partial differential equations is a wide and rapidly developing branch of contemporary mathematics. Problems related to partial differential equations of order higher than one are so diverse that a general theory can hardly be built up. There are several essentially different kinds of differential equations called elliptic, hyperbolic, and parabolic. Regarding the construction of solutions of Cauchy, mixed and boundary value problems, each kind of equation exhibits entirely different properties. Cauchy problems for hyperbolic equations and systems with variable coefficients have been studied in classical works of Petrovskii, Leret, Courant, Gording. Mixed problems for hyperbolic equations were considered by Vishik, Ladyzhenskaya, and that for general two dimensional equations were investigated by Bitsadze, Vishik, Gol'dberg, Ladyzhenskaya, Myshkis, and others. In last decade the theory of solvability on the whole of boundary value problems for nonlinear differential equations has received intensive development. Significant results for nonlinear elliptic and parabolic equations of second order were obtained in works of Gvazava, Ladyzhenskaya, Nakhushev, Oleinik, Skripnik, and others. Concerning the solvability in general of nonlinear hyperbolic equations, which are connected to the theory of local and nonlocal boundary value problems for hyperbolic equations, there are only partial results obtained by Bronshtein, Pokhozhev, Nakhushev.
Methods And Applications Of Singular Perturbations
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Author : Ferdinand Verhulst
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-06-04
Methods And Applications Of Singular Perturbations written by Ferdinand Verhulst 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 2006-06-04 with Mathematics categories.
Contains well-chosen examples and exercises A student-friendly introduction that follows a workbook type approach
Averaging Methods In Nonlinear Dynamical Systems
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Author : Jan A. Sanders
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-08-18
Averaging Methods In Nonlinear Dynamical Systems written by Jan A. Sanders 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 2007-08-18 with Mathematics categories.
Perturbation theory and in particular normal form theory has shown strong growth in recent decades. This book is a drastic revision of the first edition of the averaging book. The updated chapters represent new insights in averaging, in particular its relation with dynamical systems and the theory of normal forms. Also new are survey appendices on invariant manifolds. One of the most striking features of the book is the collection of examples, which range from the very simple to some that are elaborate, realistic, and of considerable practical importance. Most of them are presented in careful detail and are illustrated with illuminating diagrams.
Handbook Of Differential Equations Ordinary Differential Equations
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Author : Flaviano Battelli
language : en
Publisher: Elsevier
Release Date : 2008-08-19
Handbook Of Differential Equations Ordinary Differential Equations written by Flaviano Battelli and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-08-19 with Mathematics categories.
This handbook is the fourth volume in a series of volumes devoted to self-contained and up-to-date surveys in the theory of ordinary differential equations, with an additional effort to achieve readability for mathematicians and scientists from other related fields so that the chapters have been made accessible to a wider audience. Covers a variety of problems in ordinary differential equations Pure mathematical and real-world applications Written for mathematicians and scientists of many related fields
A Toolbox Of Averaging Theorems
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Author : Ferdinand Verhulst
language : en
Publisher: Springer Nature
Release Date : 2023-08-23
A Toolbox Of Averaging Theorems written by Ferdinand Verhulst and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-08-23 with Mathematics categories.
This primer on averaging theorems provides a practical toolbox for applied mathematicians, physicists, and engineers seeking to apply the well-known mathematical theory to real-world problems. With a focus on practical applications, the book introduces new approaches to dissipative and Hamiltonian resonances and approximations on timescales longer than 1/ε. Accessible and clearly written, the book includes numerous examples ranging from elementary to complex, making it an excellent basic reference for anyone interested in the subject. The prerequisites have been kept to a minimum, requiring only a working knowledge of calculus and ordinary and partial differential equations (ODEs and PDEs). In addition to serving as a valuable reference for practitioners, the book could also be used as a reading guide for a mathematics seminar on averaging methods. Whether you're an engineer, scientist, or mathematician, this book offers a wealth of practical tools and theoretical insights to help you tackle a range of mathematical problems.
Numerical Analytic Methods In Theory Of Boundary Value Problems
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Author : Miklos Ronto
language : en
Publisher: World Scientific
Release Date : 2000-06-30
Numerical Analytic Methods In Theory Of Boundary Value Problems written by Miklos Ronto and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-06-30 with Mathematics categories.
This book contains the main results of the authors' investigations on the development and application of numerical-analytic methods for ordinary nonlinear boundary value problems (BVPs). The methods under consideration provide an opportunity to solve the two important problems of the BVP theory — namely, to establish existence theorems and to build approximation solutions. They can be used to investigate a wide variety of BVPs.The Appendix, written in collaboration with S I Trofimchuk, discusses the connection of the new method with the classical Cesari, Cesari-Hale and Lyapunov-Schmidt methods.
Symmetry And Perturbation Theory Spt 98
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Author : Antonio Degasperis
language : en
Publisher: World Scientific
Release Date : 1999-12-30
Symmetry And Perturbation Theory Spt 98 written by Antonio Degasperis and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-12-30 with categories.
The second workshop on “Symmetry and Perturbation Theory” served as a forum for discussing the relations between symmetry and perturbation theory, and this put in contact rather different communities. The extension of the rigorous results of perturbation theory established for ODE's to the case of nonlinear evolution PDE's was also discussed: here a number of results are known, particularly in connection with (perturbation of) integrable systems, but there is no general frame as solidly established as in the finite-dimensional case. In aiming at such an infinite-dimensional extension, for which standard analytical tools essential in the ODE case are not available, it is natural to look primarily at geometrical and topological methods, and first of all at those based on exploiting the symmetry properties of the systems under study (both the unperturbed and the perturbed ones); moreover, symmetry considerations are in several ways basic to our understanding of integrability, i.e. finally of the unperturbed systems on whose understanding the whole of perturbation theory has unavoidably to rely.This volume contains tutorial, regular and contributed papers. The tutorial papers give students and newcomers to the field a rapid introduction to some active themes of research and recent results in symmetry and perturbation theory.
Integration On Infinite Dimensional Surfaces And Its Applications
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Author : A. Uglanov
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-29
Integration On Infinite Dimensional Surfaces And Its Applications written by A. Uglanov 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 2013-06-29 with Mathematics categories.
It seems hard to believe, but mathematicians were not interested in integration problems on infinite-dimensional nonlinear structures up to 70s of our century. At least the author is not aware of any publication concerning this theme, although as early as 1967 L. Gross mentioned that the analysis on infinite dimensional manifolds is a field of research with rather rich opportunities in his classical work [2. This prediction was brilliantly confirmed afterwards, but we shall return to this later on. In those days the integration theory in infinite dimensional linear spaces was essentially developed in the heuristic works of RP. Feynman [1], I. M. Gelfand, A. M. Yaglom [1]). The articles of J. Eells [1], J. Eells and K. D. Elworthy [1], H. -H. Kuo [1], V. Goodman [1], where the contraction of a Gaussian measure on a hypersurface, in particular, was built and the divergence theorem (the Gauss-Ostrogradskii formula) was proved, appeared only in the beginning of the 70s. In this case a Gaussian specificity was essential and it was even pointed out in a later monograph of H. -H. Kuo [3] that the surface measure for the non-Gaussian case construction problem is not simple and has not yet been solved. A. V. Skorokhod [1] and the author [6,10] offered different approaches to such a construction. Some other approaches were offered later by Yu. L. Daletskii and B. D. Maryanin [1], O. G. Smolyanov [6], N. V.
Singular Quadratic Forms In Perturbation Theory
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Author : Volodymyr Koshmanenko
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Singular Quadratic Forms In Perturbation Theory written by Volodymyr Koshmanenko 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 2012-12-06 with Mathematics categories.
The notion of singular quadratic form appears in mathematical physics as a tool for the investigation of formal expressions corresponding to perturbations devoid of operator sense. Numerous physical models are based on the use of Hamiltonians containing perturba tion terms with singular properties. Typical examples of such expressions are Schrodin ger operators with O-potentials (-~ + AD) and Hamiltonians in quantum field theory with perturbations given in terms of operators of creation and annihilation (P(
The Cumulative Book Index
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Author :
language : en
Publisher:
Release Date : 1998
The Cumulative Book Index written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998 with American literature categories.
A world list of books in the English language.