Differential Equations And Asymptotic Theory In Mathematical Physics

Author : Chen Hua,Roderick Wong
Publisher : World Scientific
Page : 388 pages
File Size : 54,8 Mb
Release : 2004-10-18
Category : Science
ISBN : 9789814481687

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Differential Equations and Asymptotic Theory in Mathematical Physics by Chen Hua,Roderick Wong Pdf

This lecture notes volume encompasses four indispensable mini courses delivered at Wuhan University with each course containing the material from five one-hour lectures. Readers are brought up to date with exciting recent developments in the areas of asymptotic analysis, singular perturbations, orthogonal polynomials, and the application of Gevrey asymptotic expansion to holomorphic dynamical systems. The book also features important invited papers presented at the conference. Leading experts in the field cover a diverse range of topics from partial differential equations arising in cancer biology to transonic shock waves. The proceedings have been selected for coverage in: • Index to Scientific & Technical Proceedings® (ISTP® / ISI Proceedings) • Index to Scientific & Technical Proceedings (ISTP CDROM version / ISI Proceedings) • CC Proceedings — Engineering & Physical Sciences Contents:Lectures on Orthogonal Polynomials (M E H Ismail)Gevrey Asymptotics and Applications to Holomorphic Ordinary Differential Equations (J-P Ramis)Spikes for Singularly Perturbed Reaction-Diffusion Systems and Carrier's Problem (M J Ward)Five Lectures on Asymptotic Theory (R S C Wong)A Perturbation Model for the Growth of Type III-V Compound Crystals (C S Bohun et al.)Asymptotic Behaviour of the Trace for Schrödinger Operator on Irregular Domains (H Chen & C Yu)Limitations and Modifications of Black-Scholes Model (L S Jiang & X M Ren)Exact Boundary Controllability of Unsteady Flows in a Network of Open Canals (T T Li)Hierarchy of Partial Differential Equations and Fundamental Solutions Associated with Summable Formal Solutions of a Partial Differential Equations of non Kowalevski Type (M Miyake & K Ichinobe)On the Singularities of Solutions of Nonlinear Partial Differential Equations in the Complex Domain, II (H Tahara)Identifying Corrosion Boundary by Perturbation Method (Y J Tan & X X Chen)Existence and Stability of Lamellar and Wriggled Lamellar Solutions in the Diblock Copolymer Problem (J C Wei) Readership: Graduate students, researchers, academics and lecturers in mathematical physics. Keywords:Asymptotic Theory;Special Functions;Orthogonal Polynomials;Singular Perturbations;Reaction Diffusion Equations;Gevrey Asymptotics;Stationary Phase Approximation;WKB Method

Author : Michael Demuth,Bert-Wolfgang Schulze
Publisher : John Wiley & Sons
Page : 436 pages
File Size : 42,7 Mb
Release : 1997
Category : Mathematics
ISBN : 3055017692

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Differential Equations, Asymptotic Analysis, and Mathematical Physics by Michael Demuth,Bert-Wolfgang Schulze Pdf

This volume contains a collection of original papers, associated with the International Conference on Partial Differential Equations, held in Potsdam, July 29 to August 2, 1996. The conference has taken place every year on a high scientific level since 1991; this event is connected with the activities of the Max Planck Research Group for Partial Differential Equations at Potsdam. Outstanding researchers and specialists from Armenia, Belarus, Belgium, Bulgaria, Canada, China, France, Germany, Great Britain, India, Israel, Italy, Japan, Poland, Romania, Russia, Spain, Sweden, Switzerland, Ukraine, and the USA contribute to this volume. The main topics concern recent progress in partial differential equations, microlocal analysis, pseudo-differential operators on manifolds with singularities, aspects in differential geometry and index theory, operator theory and operator algebras, stochastic spectral analysis, semigroups, Dirichlet forms, Schrodinger operators, semiclassical analysis, and scattering theory.

Author : Dmitrii Korikov,Boris Plamenevskii,Oleg Sarafanov
Publisher : Springer Nature
Page : 404 pages
File Size : 51,9 Mb
Release : 2021-04-01
Category : Mathematics
ISBN : 9783030653729

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Asymptotic Theory of Dynamic Boundary Value Problems in Irregular Domains by Dmitrii Korikov,Boris Plamenevskii,Oleg Sarafanov Pdf

This book considers dynamic boundary value problems in domains with singularities of two types. The first type consists of "edges" of various dimensions on the boundary; in particular, polygons, cones, lenses, polyhedra are domains of this type. Singularities of the second type are "singularly perturbed edges" such as smoothed corners and edges and small holes. A domain with singularities of such type depends on a small parameter, whereas the boundary of the limit domain (as the parameter tends to zero) has usual edges, i.e. singularities of the first type. In the transition from the limit domain to the perturbed one, the boundary near a conical point or an edge becomes smooth, isolated singular points become small cavities, and so on. In an "irregular" domain with such singularities, problems of elastodynamics, electrodynamics and some other dynamic problems are discussed. The purpose is to describe the asymptotics of solutions near singularities of the boundary. The presented results and methods have a wide range of applications in mathematical physics and engineering. The book is addressed to specialists in mathematical physics, partial differential equations, and asymptotic methods.

Author : Matthias Aschenbrenner,Lou van den Dries,Joris van der Hoeven
Publisher : Princeton University Press
Page : 880 pages
File Size : 47,9 Mb
Release : 2017-06-06
Category : Mathematics
ISBN : 9781400885411

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Asymptotic Differential Algebra and Model Theory of Transseries by Matthias Aschenbrenner,Lou van den Dries,Joris van der Hoeven Pdf

Asymptotic differential algebra seeks to understand the solutions of differential equations and their asymptotics from an algebraic point of view. The differential field of transseries plays a central role in the subject. Besides powers of the variable, these series may contain exponential and logarithmic terms. Over the last thirty years, transseries emerged variously as super-exact asymptotic expansions of return maps of analytic vector fields, in connection with Tarski's problem on the field of reals with exponentiation, and in mathematical physics. Their formal nature also makes them suitable for machine computations in computer algebra systems. This self-contained book validates the intuition that the differential field of transseries is a universal domain for asymptotic differential algebra. It does so by establishing in the realm of transseries a complete elimination theory for systems of algebraic differential equations with asymptotic side conditions. Beginning with background chapters on valuations and differential algebra, the book goes on to develop the basic theory of valued differential fields, including a notion of differential-henselianity. Next, H-fields are singled out among ordered valued differential fields to provide an algebraic setting for the common properties of Hardy fields and the differential field of transseries. The study of their extensions culminates in an analogue of the algebraic closure of a field: the Newton-Liouville closure of an H-field. This paves the way to a quantifier elimination with interesting consequences.

Author : B Vainberg
Publisher : CRC Press
Page : 516 pages
File Size : 53,7 Mb
Release : 1989-02-25
Category : Science
ISBN : 2881246648

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Asymptotic Methods in Equations of Mathematical Physics by B Vainberg Pdf

Typed English translation of a monograph first published (in Russian) in 1982. Provides graduate students and researchers with usefully detailed discussion of most of the asymptotic methods standard these days to the work of mathematical physicists. The author prefers not to dwell in the heights of abstraction; he has written a broadly intelligble book, which is informed at every point by his secure command of major physical applications. An expensive but valuable contribution to the literature of an important but too-little-written- about field. Twelve chapters, references. (NW) Annotation copyrighted by Book News, Inc., Portland, OR

Author : David Holcman,Zeev Schuss
Publisher : Springer
Page : 444 pages
File Size : 49,7 Mb
Release : 2018-05-25
Category : Mathematics
ISBN : 9783319768953

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Asymptotics of Elliptic and Parabolic PDEs by David Holcman,Zeev Schuss Pdf

This is a monograph on the emerging branch of mathematical biophysics combining asymptotic analysis with numerical and stochastic methods to analyze partial differential equations arising in biological and physical sciences. In more detail, the book presents the analytic methods and tools for approximating solutions of mixed boundary value problems, with particular emphasis on the narrow escape problem. Informed throughout by real-world applications, the book includes topics such as the Fokker-Planck equation, boundary layer analysis, WKB approximation, applications of spectral theory, as well as recent results in narrow escape theory. Numerical and stochastic aspects, including mean first passage time and extreme statistics, are discussed in detail and relevant applications are presented in parallel with the theory. Including background on the classical asymptotic theory of differential equations, this book is written for scientists of various backgrounds interested in deriving solutions to real-world problems from first principles.

Author : Carl M. Bender,Steven A. Orszag
Publisher : Springer Science & Business Media
Page : 605 pages
File Size : 46,9 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9781475730692

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Advanced Mathematical Methods for Scientists and Engineers I by Carl M. Bender,Steven A. Orszag Pdf

A clear, practical and self-contained presentation of the methods of asymptotics and perturbation theory for obtaining approximate analytical solutions to differential and difference equations. Aimed at teaching the most useful insights in approaching new problems, the text avoids special methods and tricks that only work for particular problems. Intended for graduates and advanced undergraduates, it assumes only a limited familiarity with differential equations and complex variables. The presentation begins with a review of differential and difference equations, then develops local asymptotic methods for such equations, and explains perturbation and summation theory before concluding with an exposition of global asymptotic methods. Emphasizing applications, the discussion stresses care rather than rigor and relies on many well-chosen examples to teach readers how an applied mathematician tackles problems. There are 190 computer-generated plots and tables comparing approximate and exact solutions, over 600 problems of varying levels of difficulty, and an appendix summarizing the properties of special functions.

Author : Yulia E. Karpeshina,Günter Stolz,Rudi Weikard,Yanni Zeng
Publisher : American Mathematical Soc.
Page : 410 pages
File Size : 40,6 Mb
Release : 2003
Category : Differential equations
ISBN : 9780821832967

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Advances in Differential Equations and Mathematical Physics by Yulia E. Karpeshina,Günter Stolz,Rudi Weikard,Yanni Zeng Pdf

This volume presents the proceedings of the 9th International Conference on Differential Equations and Mathematical Physics. It contains 29 research and survey papers contributed by conference participants. The conference provided researchers a forum to present and discuss their recent results in a broad range of areas encompassing the theory of differential equations and their applications in mathematical physics. Papers in this volume represent some of the most interesting results and the major areas of research that were covered, including spectral theory with applications to non-relativistic and relativistic quantum mechanics, including time-dependent and random potential, resonances, many body systems, pseudodifferential operators and quantum dynamics, inverse spectral and scattering problems, the theory of linear and nonlinear partial differential equations with applications in fluid dynamics, conservation laws and numerical simulations, as well as equilibrium and nonequilibrium statistical mechanics. The volume is intended for graduate students and researchers interested in mathematical physics.

Author : Vladimir M. Manuilov,Alexander S. Mishchenko,Vladimir E. Nazaikinskii,Bert-Wolfgang Schulze,Weiping Zhang
Publisher : Springer Nature
Page : 349 pages
File Size : 40,9 Mb
Release : 2022-01-21
Category : Mathematics
ISBN : 9783030373269

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Differential Equations on Manifolds and Mathematical Physics by Vladimir M. Manuilov,Alexander S. Mishchenko,Vladimir E. Nazaikinskii,Bert-Wolfgang Schulze,Weiping Zhang Pdf

This is a volume originating from the Conference on Partial Differential Equations and Applications, which was held in Moscow in November 2018 in memory of professor Boris Sternin and attracted more than a hundred participants from eighteen countries. The conference was mainly dedicated to partial differential equations on manifolds and their applications in mathematical physics, geometry, topology, and complex analysis. The volume contains selected contributions by leading experts in these fields and presents the current state of the art in several areas of PDE. It will be of interest to researchers and graduate students specializing in partial differential equations, mathematical physics, topology, geometry, and their applications. The readers will benefit from the interplay between these various areas of mathematics.

Author : M. V. Karasev
Publisher : American Mathematical Soc.
Page : 298 pages
File Size : 50,9 Mb
Release : 2003
Category : Asymptotic symmetry (Physics)
ISBN : 0821833367

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Asymptotic Methods for Wave and Quantum Problems by M. V. Karasev Pdf

The collection consists of four papers in different areas of mathematical physics united by the intrinsic coherence of the asymptotic methods used. The papers describe both the known results and most recent achievements, as well as new concepts and ideas in mathematical analysis of quantum and wave problems. In the introductory paper ``Quantization and Intrinsic Dynamics'' a relationship between quantization of symplectic manifolds and nonlinear wave equations is described and discussed from the viewpoint of the weak asymptotics method (asymptotics in distributions) and the semiclassical approximation method. It also explains a hidden dynamic geometry that arises when using these methods. Three other papers discuss applications of asymptotic methods to the construction of wave-type solutions of nonlinear PDE's, to the theory of semiclassical approximation (in particular, the Whitham method) for nonlinear second-order ordinary differential equations, and to the study of the Schrodinger type equations whose potential wells are sufficiently shallow that the discrete spectrum contains precisely one point. All the papers contain detailed references and are oriented not only to specialists in asymptotic methods, but also to a wider audience of researchers and graduate students working in partial differential equations and mathematical physics.

Author : M.V. Fedoryuk
Publisher : Springer Science & Business Media
Page : 248 pages
File Size : 47,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642584237

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Partial Differential Equations V by M.V. Fedoryuk Pdf

In this paper we shall discuss the construction of formal short-wave asymp totic solutions of problems of mathematical physics. The topic is very broad. It can somewhat conveniently be divided into three parts: 1. Finding the short-wave asymptotics of a rather narrow class of problems, which admit a solution in an explicit form, via formulas that represent this solution. 2. Finding formal asymptotic solutions of equations that describe wave processes by basing them on some ansatz or other. We explain what 2 means. Giving an ansatz is knowing how to give a formula for the desired asymptotic solution in the form of a series or some expression containing a series, where the analytic nature of the terms of these series is indicated up to functions and coefficients that are undetermined at the first stage of consideration. The second stage is to determine these functions and coefficients using a direct substitution of the ansatz in the equation, the boundary conditions and the initial conditions. Sometimes it is necessary to use different ansiitze in different domains, and in the overlapping parts of these domains the formal asymptotic solutions must be asymptotically equivalent (the method of matched asymptotic expansions). The basis for success in the search for formal asymptotic solutions is a suitable choice of ansiitze. The study of the asymptotics of explicit solutions of special model problems allows us to "surmise" what the correct ansiitze are for the general solution.

Author : Isaak Rubinstein,Lev Rubinstein
Publisher : Cambridge University Press
Page : 704 pages
File Size : 51,7 Mb
Release : 1998-04-28
Category : Mathematics
ISBN : 0521558468

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Partial Differential Equations in Classical Mathematical Physics by Isaak Rubinstein,Lev Rubinstein Pdf

The unique feature of this book is that it considers the theory of partial differential equations in mathematical physics as the language of continuous processes, that is, as an interdisciplinary science that treats the hierarchy of mathematical phenomena as reflections of their physical counterparts. Special attention is drawn to tracing the development of these mathematical phenomena in different natural sciences, with examples drawn from continuum mechanics, electrodynamics, transport phenomena, thermodynamics, and chemical kinetics. At the same time, the authors trace the interrelation between the different types of problems - elliptic, parabolic, and hyperbolic - as the mathematical counterparts of stationary and evolutionary processes. This combination of mathematical comprehensiveness and natural scientific motivation represents a step forward in the presentation of the classical theory of PDEs, one that will be appreciated by both students and researchers alike.

Author : M. H. Lantsman
Publisher : Unknown
Page : 452 pages
File Size : 51,8 Mb
Release : 2014-01-15
Category : Electronic
ISBN : 9401597987

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Asymptotics of Linear Differential Equations by M. H. Lantsman Pdf

Author : David Y. Gao,Vadim A. Krysko
Publisher : CRC Press
Page : 272 pages
File Size : 52,5 Mb
Release : 2006-05-03
Category : Mathematics
ISBN : 9781420011739

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Introduction to Asymptotic Methods by David Y. Gao,Vadim A. Krysko Pdf

Among the theoretical methods for solving many problems of applied mathematics, physics, and technology, asymptotic methods often provide results that lead to obtaining more effective algorithms of numerical evaluation. Presenting the mathematical methods of perturbation theory, Introduction to Asymptotic Methods reviews the most important m

Author : O. A. Oleĭnik
Publisher : Cambridge University Press
Page : 218 pages
File Size : 53,9 Mb
Release : 1996-03-21
Category : Mathematics
ISBN : 0521485371

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Some Asymptotic Problems in the Theory of Partial Differential Equations by O. A. Oleĭnik Pdf

In 1993, Professor Oleinik was invited to give a series of lectures about her work in the area of partial differential equations. This book contains those lectures, and more.