Lectures on Cauchy's Problem in Linear Partial Differential Equations PDF Download

Author: Jacques Hadamard
Publisher:
ISBN:
Category : Cauchy problem
Languages : en
Pages : 336

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Author: Hector O. Fattorini
Publisher: Cambridge University Press
ISBN: 0521302382
Category : Mathematics
Languages : en
Pages : 664

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Book Description
This volume deals with the Cauchy or initial value problem for linear differential equations. It treats in detail some of the applications of linear space methods to partial differential equations, especially the equations of mathematical physics such as the Maxwell, Schrödinger and Dirac equations. Background material presented in the first chapter makes the book accessible to mathematicians and physicists who are not specialists in this area as well as to graduate students.

Author: F. J. Bureau
Publisher:
ISBN:
Category : Cauchy problem
Languages : en
Pages : 186

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Author: Tatsuo Nishitani
Publisher: Springer
ISBN: 3319676121
Category : Mathematics
Languages : en
Pages : 215

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Book Description
Combining geometrical and microlocal tools, this monograph gives detailed proofs of many well/ill-posed results related to the Cauchy problem for differential operators with non-effectively hyperbolic double characteristics. Previously scattered over numerous different publications, the results are presented from the viewpoint that the Hamilton map and the geometry of bicharacteristics completely characterizes the well/ill-posedness of the Cauchy problem. A doubly characteristic point of a differential operator P of order m (i.e. one where Pm = dPm = 0) is effectively hyperbolic if the Hamilton map FPm has real non-zero eigen values. When the characteristics are at most double and every double characteristic is effectively hyperbolic, the Cauchy problem for P can be solved for arbitrary lower order terms. If there is a non-effectively hyperbolic characteristic, solvability requires the subprincipal symbol of P to lie between −Pμj and Pμj , where iμj are the positive imaginary eigenvalues of FPm . Moreover, if 0 is an eigenvalue of FPm with corresponding 4 × 4 Jordan block, the spectral structure of FPm is insufficient to determine whether the Cauchy problem is well-posed and the behavior of bicharacteristics near the doubly characteristic manifold plays a crucial role.

Author: Jan F. van Diejen
Publisher: Springer Science & Business Media
ISBN: 1461212065
Category : Science
Languages : en
Pages : 572

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In the 1970s F. Calogero and D. Sutherland discovered that for certain potentials in one-dimensional systems, but for any number of particles, the Schrödinger eigenvalue problem is exactly solvable. Until then, there was only one known nontrivial example of an exactly solvable quantum multi-particle problem. J. Moser subsequently showed that the classical counterparts to these models is also amenable to an exact analytical approach. The last decade has witnessed a true explosion of activities involving Calogero-Moser-Sutherland models, and these now play a role in research areas ranging from theoretical physics (such as soliton theory, quantum field theory, string theory, solvable models of statistical mechanics, condensed matter physics, and quantum chaos) to pure mathematics (such as representation theory, harmonic analysis, theory of special functions, combinatorics of symmetric functions, dynamical systems, random matrix theory, and complex geometry). The aim of this volume is to provide an overview of the many branches into which research on CMS systems has diversified in recent years. The contributions are by leading researchers from various disciplines in whose work CMS systems appear, either as the topic of investigation itself or as a tool for further applications.

Author: N. G. Basov
Publisher: Springer Science & Business Media
ISBN: 1468406760
Category : Science
Languages : en
Pages : 191

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This collection contains survey articles dealing with the following topics: The Mach principle and its role in the general theory of relativity, the modern conception of the vacuum, new methods in the theory of Lie group representations, the coherent state method and its application to physical problems, and the Newman-Penrose method and its application to problems in general relativity theory.

Author: Charles R. Strom
Publisher:
ISBN:
Category : Aerodynamics
Languages : en
Pages : 136

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Book Description
The method of characteristics is formulated for the computation of the supersonic flow of an inviscid, reacting gas over a smooth three-dimensional body. Various methods of constructing networks of bicharacteristic lines are examined from the point of view of numerical stability and accuracy. A new method of forming the network, which consists of projecting forward along streamlines from data points on specified data planes, is found to be most easily adopted to the particular requirements of nonequilibrium chemistry. The general method was coded for the IBM 7090 computer and the program demonstrated for the case of an ideal gas. Calculations were made for the case of an ideal gas. Calculations were made for the flow about a spherical-tip 15 degree half-angle cone at 10 degree angle of attack and a generalized elliptical body at zero incidence. Since the program yields the pressure distribution along specified streamlines, it is straightforward, in principle, to link it to a finite-rate chemistry stream tube program to treat three-dimensional, nonequilibrium flows. (Author).

Author: Reiko Sakamoto
Publisher: CUP Archive
ISBN: 9780521235686
Category : Mathematics
Languages : en
Pages : 232

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Book Description
Boundary value problems are of central importance and interest not only to mathematicians but also to physicists and engineers who need to solve differential equations which govern the behaviour of physical systems. In this book, Professor Sakamoto introduces the general theory of the existence and uniqueness of solutions to the wave equation. The reader is assumed to have some familiarity with Lebesgue integration and complex function theory but other than that the book is essentially self-contained. It is therefore suited to senior undergraduates and graduates in mathematics and the mathematical sciences but can be read with profit by professionals in those subjects.

Author: S. L. Sobolev
Publisher: American Mathematical Soc.
ISBN: 9780821898321
Category : Mathematics
Languages : en
Pages : 300

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Book Description
Special problems of functional analysis Variational methods in mathematical physics The theory of hyperbolic partial differential equations Comments Appendix: Methode nouvelle a resoudre le probleme de Cauchy pour les equations lineaires hyperboliques normales Comments on the appendix Bibliography Index

Author: W. M. Wonham
Publisher: Springer Science & Business Media
ISBN: 1468400681
Category : Science
Languages : en
Pages : 340

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Book Description
In writing this monograph my aim has been to present a "geometric" approach to the structural synthesis of multivariable control systems that are linear, time-invariant and of finite dynamic order. The book is addressed to graduate students specializing in control, to engineering scientists engaged in control systems research and development, and to mathemati cians with some previous acquaintance with control problems. The present edition of this book is a revision of the preliminary version, published in 1974 as a Springer-Verlag "Lecture Notes" volume; and some of the remarks to follow are repeated from the original preface. The label "geometric" in the title is applied for several reasons. First and obviously, the setting is linear state space and the mathematics chiefly linear algebra in abstract (geometric) style. The basic ideas are the familiar system concepts of controllability and observability, thought of as geometric properties of distinguished state subspaces. Indeed, the geometry was first brought in out of revulsion against the orgy of matrix manipulation which linear control theory mainly consisted of, not so long ago. But secondly and of greater interest, the geometric setting rather quickly suggested new methods of attacking synthesis which have proved to be intuitive and econo mical; they are also easily reduced to matrix arithmetic as soon as you want to compute.