Differential Equations Asymptotic Theory In Mathematical Physics
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Differential Equations And Asymptotic Theory In Mathematical Physics
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Author : Chen Hua
language : en
Publisher: World Scientific
Release Date : 2004-10-18
Differential Equations And Asymptotic Theory In Mathematical Physics written by Chen Hua and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-10-18 with Science categories.
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
Differential Equations Asymptotic Analysis And Mathematical Physics
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Author : Michael Demuth
language : en
Publisher: John Wiley & Sons
Release Date : 1997
Differential Equations Asymptotic Analysis And Mathematical Physics written by Michael Demuth and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997 with Mathematics categories.
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.
Asymptotic Theory Of Dynamic Boundary Value Problems In Irregular Domains
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Author : Dmitrii Korikov
language : en
Publisher: Springer Nature
Release Date : 2021-04-01
Asymptotic Theory Of Dynamic Boundary Value Problems In Irregular Domains written by Dmitrii Korikov and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-04-01 with Mathematics categories.
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.
Asymptotic Methods In Equations Of Mathematical Physics
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Author : B Vainberg
language : en
Publisher: CRC Press
Release Date : 1989-02-25
Asymptotic Methods In Equations Of Mathematical Physics written by B Vainberg and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989-02-25 with Science categories.
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
Asymptotic Differential Algebra And Model Theory Of Transseries
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Author : Matthias Aschenbrenner
language : en
Publisher: Princeton University Press
Release Date : 2017-06-06
Asymptotic Differential Algebra And Model Theory Of Transseries written by Matthias Aschenbrenner and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-06-06 with Mathematics categories.
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.
Asymptotics Of Elliptic And Parabolic Pdes
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Author : David Holcman
language : en
Publisher: Springer
Release Date : 2018-05-25
Asymptotics Of Elliptic And Parabolic Pdes written by David Holcman and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-05-25 with Mathematics categories.
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.
Advanced Mathematical Methods For Scientists And Engineers I
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Author : Carl M. Bender
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
Advanced Mathematical Methods For Scientists And Engineers I written by Carl M. Bender 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 2013-03-09 with Mathematics categories.
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.
Asymptotics Of Linear Differential Equations
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Author : M. H. Lantsman
language : en
Publisher:
Release Date : 2014-01-15
Asymptotics Of Linear Differential Equations written by M. H. Lantsman and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-15 with categories.
Asymptotic Methods For Wave And Quantum Problems
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Author : M. V. Karasev
language : en
Publisher: American Mathematical Soc.
Release Date : 2003
Asymptotic Methods For Wave And Quantum Problems written by M. V. Karasev 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 2003 with Asymptotic symmetry (Physics) categories.
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.
Asymptotic Theory Of Elliptic Boundary Value Problems In Singularly Perturbed Domains
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Author : Vladimir Maz'ya
language : en
Publisher: Springer Science & Business Media
Release Date : 2000-05-01
Asymptotic Theory Of Elliptic Boundary Value Problems In Singularly Perturbed Domains written by Vladimir Maz'ya 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 2000-05-01 with Mathematics categories.
For the first time in the mathematical literature, this two-volume work introduces a unified and general approach to the subject. To a large extent, the book is based on the authors’ work, and has no significant overlap with other books on the theory of elliptic boundary value problems.