Equations of the Mixed Type
Equations of the Mixed Type

Author: A. V. Bitsadze

Publisher: Elsevier

Published: 2014-05-16

Total Pages: 177

ISBN-13: 1483164861

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Equations of the Mixed Type compiles a series of lectures on certain fundamental questions in the theory of equations of mixed type. This book investigates the series of problems concerning linear partial differential equations of the second order in two variables, and possessing the property that the type of the equation changes either on the boundary of or inside the considered domain. Topics covered include general remarks on linear partial differential equations of mixed type; study of the solutions of second order hyperbolic equations with initial conditions given along the lines of parabolicity; and study of the solutions of second order elliptic equations for a domain, the boundary of which includes a segment of the curve of parabolic degeneracy. The problem of Tricomi and other mixed problems are also deliberated in this text. This publication is a good reference for students and researchers conducting work on the theory of equations of mixed type.

Lecture Notes on Mixed Type Partial Differential Equations
Lecture Notes on Mixed Type Partial Differential Equations

Author: John Michael Rassias

Publisher: World Scientific

Published: 1990

Total Pages: 160

ISBN-13: 9789810204068

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This book discusses various parts of the theory of mixed type partial differential equations with boundary conditions such as: Chaplygin's classical dynamical equation of mixed type, the theory of regularity of solutions in the sense of Tricomi, Tricomi's fundamental idea and one-dimensional singular integral equations on non-Carleman type, Gellerstedt's characteristic problem and Frankl's non-characteristic problem, Bitsadze and Lavrentjev's mixed type boundary value problems, quasi-regularity of solutions in the classical sense. Some of the latest results of the author are also presented in this book.

Mixed Type Partial Differential Equations, Lecture Notes On
Mixed Type Partial Differential Equations, Lecture Notes On

Author: Rassias John Michael

Publisher: World Scientific Publishing Company

Published: 1990-08-30

Total Pages: 152

ISBN-13: 9813103647

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This book discusses various parts of the theory of mixed type partial differential equations with boundary conditions such as: Chaplygin's classical dynamical equation of mixed type, the theory of regularity of solutions in the sense of Tricomi, Tricomi's fundamental idea and one-dimensional singular integral equations on non-Carleman type, Gellerstedt's characteristic problem and Frankl's non-characteristic problem, Bitsadze and Lavrentjev's mixed type boundary value problems, quasi-regularity of solutions in the classical sense. Some of the latest results of the author are also presented in this book.

Linear and Quasilinear Complex Equations of Hyperbolic and Mixed Types
Linear and Quasilinear Complex Equations of Hyperbolic and Mixed Types

Author: Guo Chun Wen

Publisher: CRC Press

Published: 2002-08-22

Total Pages: 272

ISBN-13: 0203166582

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This volume deals with first and second order complex equations of hyperbolic and mixed types. Various general boundary value problems for linear and quasilinear complex equations are investigated in detail. To obtain results for complex equations of mixed types, some discontinuous boundary value problems for elliptic complex equations are discusse

A Practical Course in Differential Equations and Mathematical Modelling
A Practical Course in Differential Equations and Mathematical Modelling

Author: Nail H. Ibragimov

Publisher: World Scientific

Published: 2009

Total Pages: 365

ISBN-13: 9814291951

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A Practical Course in Differential Equations and Mathematical Modelling is a unique blend of the traditional methods of ordinary and partial differential equations with Lie group analysis enriched by the author?s own theoretical developments. The book ? which aims to present new mathematical curricula based on symmetry and invariance principles ? is tailored to develop analytic skills and ?working knowledge? in both classical and Lie?s methods for solving linear and nonlinear equations. This approach helps to make courses in differential equations, mathematical modelling, distributions and fundamental solution, etc. easy to follow and interesting for students. The book is based on the author?s extensive teaching experience at Novosibirsk and Moscow universities in Russia, CollŠge de France, Georgia Tech and Stanford University in the United States, universities in South Africa, Cyprus, Turkey, and Blekinge Institute of Technology (BTH) in Sweden. The new curriculum prepares students for solving modern nonlinear problems and will essentially be more appealing to students compared to the traditional way of teaching mathematics.

Partial Differential Equations in China
Partial Differential Equations in China

Author: Chaohao Gu

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 193

ISBN-13: 9401111987

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In the past few years there has been a fruitful exchange of expertise on the subject of partial differential equations (PDEs) between mathematicians from the People's Republic of China and the rest of the world. The goal of this collection of papers is to summarize and introduce the historical progress of the development of PDEs in China from the 1950s to the 1980s. The results presented here were mainly published before the 1980s, but, having been printed in the Chinese language, have not reached the wider audience they deserve. Topics covered include, among others, nonlinear hyperbolic equations, nonlinear elliptic equations, nonlinear parabolic equations, mixed equations, free boundary problems, minimal surfaces in Riemannian manifolds, microlocal analysis and solitons. For mathematicians and physicists interested in the historical development of PDEs in the People's Republic of China.

The Dirichlet Problem for Elliptic-Hyperbolic Equations of Keldysh Type
The Dirichlet Problem for Elliptic-Hyperbolic Equations of Keldysh Type

Author: Thomas H. Otway

Publisher: Springer Science & Business Media

Published: 2012-01-07

Total Pages: 219

ISBN-13: 3642244149

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Partial differential equations of mixed elliptic-hyperbolic type arise in diverse areas of physics and geometry, including fluid and plasma dynamics, optics, cosmology, traffic engineering, projective geometry, geometric variational theory, and the theory of isometric embeddings. And yet even the linear theory of these equations is at a very early stage. This text examines various Dirichlet problems which can be formulated for equations of Keldysh type, one of the two main classes of linear elliptic-hyperbolic equations. Open boundary conditions (in which data are prescribed on only part of the boundary) and closed boundary conditions (in which data are prescribed on the entire boundary) are both considered. Emphasis is on the formulation of boundary conditions for which solutions can be shown to exist in an appropriate function space. Specific applications to plasma physics, optics, and analysis on projective spaces are discussed. (From the preface)

Lipman Bers, a Life in Mathematics
Lipman Bers, a Life in Mathematics

Author: Linda Keen

Publisher: American Mathematical Soc.

Published: 2015-09-15

Total Pages: 362

ISBN-13: 1470420562

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The book is part biography and part collection of mathematical essays that gives the reader a perspective on the evolution of an interesting mathematical life. It is all about Lipman Bers, a giant in the mathematical world who lived in turbulent and exciting times. It captures the essence of his mathematics, a development and transition from applied mathematics to complex analysis--quasiconformal mappings and moduli of Riemann surfaces--and the essence of his personality, a progression from a young revolutionary refugee to an elder statesman in the world of mathematics and a fighter for global human rights and the end of political torture. The book contains autobiographical material and short reprints of his work. The main content is in the exposition of his research contributions, sometimes with novel points of view, by students, grand-students, and colleagues. The research described was fundamental to the growth of a central part of 20th century mathematics that, now in the 21st century, is in a healthy state with much current interest and activity. The addition of personal recollections, professional tributes, and photographs yields a picture of a man, his personal and professional family, and his time.