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Some Asymptotic Problems In The Theory Of Partial Differential Equations
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Book Synopsis Some Asymptotic Problems in the Theory of Partial Differential Equations by : O. A. Oleĭnik
Download or read book Some Asymptotic Problems in the Theory of Partial Differential Equations written by O. A. Oleĭnik and published by Cambridge University Press. This book was released on 1996-03-21 with total page 218 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Asymptotic Issues For Some Partial Differential Equations (Second Edition) by : Michel Marie Chipot
Download or read book Asymptotic Issues For Some Partial Differential Equations (Second Edition) written by Michel Marie Chipot and published by World Scientific. This book was released on 2024-04-15 with total page 283 pages. Available in PDF, EPUB and Kindle. Book excerpt: The primary focus of the book is to explore the asymptotic behavior of problems formulated within cylindrical structures. Various physical applications are discussed, with certain topics such as fluid flows in channels being particularly noteworthy. Additionally, the book delves into the relevance of elasticity in the context of cylindrical bodies.In specific scenarios where the size of the cylinder becomes exceptionally large, the material's behavior is determined solely by its cross-section. The investigation centers around understanding these particular properties.Since the publication of the first edition, several significant advancements have been made, adding depth and interest to the content. Consequently, new sections have been incorporated into the existing edition, complemented by a comprehensive list of references.
Book Synopsis Asymptotic Theory of Dynamic Boundary Value Problems in Irregular Domains by : Dmitrii Korikov
Download or read book Asymptotic Theory of Dynamic Boundary Value Problems in Irregular Domains written by Dmitrii Korikov and published by Springer Nature. This book was released on 2021-04-01 with total page 404 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Markov Processes and Differential Equations by : Mark I. Freidlin
Download or read book Markov Processes and Differential Equations written by Mark I. Freidlin and published by Birkhäuser. This book was released on 2012-12-06 with total page 155 pages. Available in PDF, EPUB and Kindle. Book excerpt: Probabilistic methods can be applied very successfully to a number of asymptotic problems for second-order linear and non-linear partial differential equations. Due to the close connection between the second order differential operators with a non-negative characteristic form on the one hand and Markov processes on the other, many problems in PDE's can be reformulated as problems for corresponding stochastic processes and vice versa. In the present book four classes of problems are considered: - the Dirichlet problem with a small parameter in higher derivatives for differential equations and systems - the averaging principle for stochastic processes and PDE's - homogenization in PDE's and in stochastic processes - wave front propagation for semilinear differential equations and systems. From the probabilistic point of view, the first two topics concern random perturbations of dynamical systems. The third topic, homog- enization, is a natural problem for stochastic processes as well as for PDE's. Wave fronts in semilinear PDE's are interesting examples of pattern formation in reaction-diffusion equations. The text presents new results in probability theory and their applica- tion to the above problems. Various examples help the reader to understand the effects. Prerequisites are knowledge in probability theory and in partial differential equations.
Book Synopsis Asymptotic Issues for Some Partial Differential Equations by : Michel Chipot
Download or read book Asymptotic Issues for Some Partial Differential Equations written by Michel Chipot and published by . This book was released on 2016 with total page 252 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Asymptotic Behavior and Stability Problems in Ordinary Differential Equations by : Lamberto Cesari
Download or read book Asymptotic Behavior and Stability Problems in Ordinary Differential Equations written by Lamberto Cesari and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the last few decades the theory of ordinary differential equations has grown rapidly under the action of forces which have been working both from within and without: from within, as a development and deepen ing of the concepts and of the topological and analytical methods brought about by LYAPUNOV, POINCARE, BENDIXSON, and a few others at the turn of the century; from without, in the wake of the technological development, particularly in communications, servomechanisms, auto matic controls, and electronics. The early research of the authors just mentioned lay in challenging problems of astronomy, but the line of thought thus produced found the most impressive applications in the new fields. The body of research now accumulated is overwhelming, and many books and reports have appeared on one or another of the multiple aspects of the new line of research which some authors call" qualitative theory of differential equations". The purpose of the present volume is to present many of the view points and questions in a readable short report for which completeness is not claimed. The bibliographical notes in each section are intended to be a guide to more detailed expositions and to the original papers. Some traditional topics such as the Sturm comparison theory have been omitted. Also excluded were all those papers, dealing with special differential equations motivated by and intended for the applications.
Book Synopsis Free Boundary Problems and Asymptotic Behavior of Singularly Perturbed Partial Differential Equations by : Kelei Wang
Download or read book Free Boundary Problems and Asymptotic Behavior of Singularly Perturbed Partial Differential Equations written by Kelei Wang and published by Springer Science & Business Media. This book was released on 2014-07-08 with total page 117 pages. Available in PDF, EPUB and Kindle. Book excerpt: This thesis is devoted to the study of the asymptotic behavior of singularly perturbed partial differential equations and some related free boundary problems arising from these two problems. We study the free boundary problems in the singulary limit and give some characterizations, and use this to study the dynamical behavior of competing species when the competition is strong. These results have many applications in physics and biology.
Book Synopsis Optimal Control Problems for Partial Differential Equations on Reticulated Domains by : Peter I. Kogut
Download or read book Optimal Control Problems for Partial Differential Equations on Reticulated Domains written by Peter I. Kogut and published by Springer Science & Business Media. This book was released on 2011-09-09 with total page 639 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the development of optimal control, the complexity of the systems to which it is applied has increased significantly, becoming an issue in scientific computing. In order to carry out model-reduction on these systems, the authors of this work have developed a method based on asymptotic analysis. Moving from abstract explanations to examples and applications with a focus on structural network problems, they aim at combining techniques of homogenization and approximation. Optimal Control Problems for Partial Differential Equations on Reticulated Domains is an excellent reference tool for graduate students, researchers, and practitioners in mathematics and areas of engineering involving reticulated domains.
Book Synopsis Asymptotic and Numerical Methods for Partial Differential Equations with Critical Parameters by : H.G. Kaper
Download or read book Asymptotic and Numerical Methods for Partial Differential Equations with Critical Parameters written by H.G. Kaper and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 371 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the NATO Advanced Research Workshop on "Asymptotic-induced Numerical Methods for Partial Differ ential Equations, Critical Parameters, and Domain Decomposition," held at Beaune (France), May 25-28, 1992. The purpose of the workshop was to stimulate the integration of asymp totic analysis, domain decomposition methods, and symbolic manipulation tools for the numerical solution of partial differential equations (PDEs) with critical parameters. A workshop on the same topic was held at Argonne Na tional Laboratory in February 1990. (The proceedings were published under the title Asymptotic Analysis and the Numerical Solu.tion of Partial Differ ential Equations, Hans G. Kaper and Marc Garbey, eds., Lecture Notes in Pure and Applied Mathematics. Vol. 130, ·Marcel Dekker, Inc., New York, 1991.) In a sense, the present proceedings represent a progress report on the topic area. Comparing the two sets of proceedings, we see an increase in the quantity as well as the quality of the contributions. 110re research is being done in the topic area, and the interest covers serious, nontrivial problems. We are pleased with this outcome and expect to see even more advances in the next few years as the field progresses.
Book Synopsis Differential Equations And Asymptotic Theory In Mathematical Physics by : Hua Chen
Download or read book Differential Equations And Asymptotic Theory In Mathematical Physics written by Hua Chen and published by World Scientific. This book was released on 2004-10-18 with total page 389 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Book Synopsis Differential Equations, Asymptotic Analysis, and Mathematical Physics by : Michael Demuth
Download or read book Differential Equations, Asymptotic Analysis, and Mathematical Physics written by Michael Demuth and published by John Wiley & Sons. This book was released on 1997 with total page 436 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Introduction to the General Theory of Singular Perturbations by : S. A. Lomov
Download or read book Introduction to the General Theory of Singular Perturbations written by S. A. Lomov and published by American Mathematical Soc.. This book was released on with total page 402 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is aimed at researchers and students in physics, mathematics, and engineering. It contains the first systematic presentation of a general approach to the integration of singularly perturbed differential equations describing nonuniform transitions, such as the occurrence of a boundary layer, discontinuities, boundary effects and so on. The method of regularization of singular perturbations presented here can be applied to the asymptotic integration of systems of ordinary and partial differential equations.
Book Synopsis Asymptotic Analysis and the Numerical Solution of Partial Differential Equations by : Hans G. Kaper
Download or read book Asymptotic Analysis and the Numerical Solution of Partial Differential Equations written by Hans G. Kaper and published by CRC Press. This book was released on 1991-02-25 with total page 288 pages. Available in PDF, EPUB and Kindle. Book excerpt: Integrates two fields generally held to be incompatible, if not downright antithetical, in 16 lectures from a February 1990 workshop at the Argonne National Laboratory, Illinois. The topics, of interest to industrial and applied mathematicians, analysts, and computer scientists, include singular per
Book Synopsis Spectral Theory and Asymptotics of Differential Equations by :
Download or read book Spectral Theory and Asymptotics of Differential Equations written by and published by Elsevier. This book was released on 2011-09-21 with total page 219 pages. Available in PDF, EPUB and Kindle. Book excerpt: Spectral Theory and Asymptotics of Differential Equations
Book Synopsis Partial Differential Equations V by : M.V. Fedoryuk
Download or read book Partial Differential Equations V written by M.V. Fedoryuk and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Partial Differential Equations by : J. Necas
Download or read book Partial Differential Equations written by J. Necas and published by Routledge. This book was released on 2018-05-04 with total page 358 pages. Available in PDF, EPUB and Kindle. Book excerpt: As a satellite conference of the 1998 International Mathematical Congress and part of the celebration of the 650th anniversary of Charles University, the Partial Differential Equations Theory and Numerical Solution conference was held in Prague in August, 1998. With its rich scientific program, the conference provided an opportunity for almost 200 participants to gather and discuss emerging directions and recent developments in partial differential equations (PDEs). This volume comprises the Proceedings of that conference. In it, leading specialists in partial differential equations, calculus of variations, and numerical analysis present up-to-date results, applications, and advances in numerical methods in their fields. Conference organizers chose the contributors to bring together the scientists best able to present a complex view of problems, starting from the modeling, passing through the mathematical treatment, and ending with numerical realization. The applications discussed include fluid dynamics, semiconductor technology, image analysis, motion analysis, and optimal control. The importance and quantity of research carried out around the world in this field makes it imperative for researchers, applied mathematicians, physicists and engineers to keep up with the latest developments. With its panel of international contributors and survey of the recent ramifications of theory, applications, and numerical methods, Partial Differential Equations: Theory and Numerical Solution provides a convenient means to that end.
Book Synopsis Partial Differential Equations V by : M.V. Fedoryuk
Download or read book Partial Differential Equations V written by M.V. Fedoryuk and published by Springer. This book was released on 2011-09-27 with total page 247 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
