Some Asymptotic Problems In The Theory Of Partial Differential Equations

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Some Asymptotic Problems In The Theory Of Partial Differential Equations

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Author : O. A. Oleĭnik
language : en
Publisher: Cambridge University Press
Release Date : 1996-03-21

Some Asymptotic Problems In The Theory Of Partial Differential Equations written by O. A. Oleĭnik and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996-03-21 with Mathematics categories.

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.

Partial Differential Equations In Classical Mathematical Physics

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Author : Isaak Rubinstein
language : en
Publisher: Cambridge University Press
Release Date : 1998-04-28

Partial Differential Equations In Classical Mathematical Physics written by Isaak Rubinstein and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-04-28 with Mathematics categories.

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.

Markov Processes And Differential Equations

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Author : Mark I. Freidlin
language : en
Publisher: Springer Science & Business Media
Release Date : 1996-03-28

Markov Processes And Differential Equations written by Mark I. Freidlin 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 1996-03-28 with Mathematics categories.

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.

Asymptotic Behavior And Stability Problems In Ordinary Differential Equations

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Author : Lamberto Cesari
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Asymptotic Behavior And Stability Problems In Ordinary Differential Equations written by Lamberto Cesari 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.

This second edition, which has become necessary within so short a time, presents no major changes. However new results in the line of work of the author and of J. K. HaIe have made it advisable to rewrite seetion (8.5). Also, some references to most recent work have been added. LAMBERTO CESARI University of Michigan June 1962 Ann Arbor Preface to the First Edition 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 matie 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.

Nonlinear Partial Differential Equations

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Author : Mi-Ho Giga
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-05-30

Nonlinear Partial Differential Equations written by Mi-Ho Giga 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 2010-05-30 with Mathematics categories.

This work will serve as an excellent first course in modern analysis. The main focus is on showing how self-similar solutions are useful in studying the behavior of solutions of nonlinear partial differential equations, especially those of parabolic type. This textbook will be an excellent resource for self-study or classroom use.

Asymptotic Expansions For Ordinary Differential Equations

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Author : Wolfgang Wasow
language : en
Publisher: Courier Dover Publications
Release Date : 2018-03-21

Asymptotic Expansions For Ordinary Differential Equations written by Wolfgang Wasow and has been published by Courier Dover Publications this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-03-21 with Mathematics categories.

This outstanding text concentrates on the mathematical ideas underlying various asymptotic methods for ordinary differential equations that lead to full, infinite expansions. "A book of great value." — Mathematical Reviews. 1976 revised edition.

Perturbation Of The Boundary In Boundary Value Problems Of Partial Differential Equations

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Author : Dan Henry
language : en
Publisher: Cambridge University Press
Release Date : 2005-05-26

Perturbation Of The Boundary In Boundary Value Problems Of Partial Differential Equations written by Dan Henry and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-05-26 with Mathematics categories.

This book, first published in 2005, works to answer a wide range of problems involving boundary perturbations in the study of partial differential equations.

Geometry In Partial Differential Equations

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Author : Agostino Prastaro
language : en
Publisher: World Scientific
Release Date : 1994

Geometry In Partial Differential Equations written by Agostino Prastaro and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994 with Mathematics categories.

This book emphasizes the interdisciplinary interaction in problems involving geometry and partial differential equations. It provides an attempt to follow certain threads that interconnect various approaches in the geometric applications and influence of partial differential equations. A few such approaches include: Morse-Palais-Smale theory in global variational calculus, general methods to obtain conservation laws for PDEs, structural investigation for the understanding of the meaning of quantum geometry in PDEs, extensions to super PDEs (formulated in the category of supermanifolds) of the geometrical methods just introduced for PDEs and the harmonic theory which proved to be very important especially after the appearance of the Atiyah-Singer index theorem, which provides a link between geometry and topology.

Asymptotic Analysis Of Differential Equations

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Author : Roscoe B. White
language : en
Publisher: World Scientific
Release Date : 2005

Asymptotic Analysis Of Differential Equations written by Roscoe B. White and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with categories.

Differential Equations Asymptotic Theory In Mathematical Physics

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Author : Zhen Hua
language : en
Publisher: World Scientific
Release Date : 2004

Differential Equations Asymptotic Theory In Mathematical Physics written by Zhen 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 with Mathematics 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