Partial Differential Equations And Spectral Theory

Author: Michael Demuth
Publisher: Springer Science & Business Media
ISBN: 9783034800242
Size: 24.84 MB
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This volume collects six articles on selected topics at the frontier between partial differential equations and spectral theory, written by leading specialists in their respective field. The articles focus on topics that are in the center of attention of current research, with original contributions from the authors. They are written in a clear expository style that makes them accessible to a broader audience. The articles contain a detailed introduction and discuss recent progress, provide additional motivation, and develop the necessary tools. Moreover, the authors share their views on future developments, hypotheses, and unsolved problems.

Nonlinear Hyperbolic Equations Spectral Theory And Wavelet Transformations

Author: Sergio Albeverio
Publisher: Birkhäuser
ISBN: 3034880731
Size: 51.95 MB
Format: PDF
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This volume focuses on recent developments in non-linear and hyperbolic equations. It will be a most valuable resource for researchers in applied mathematics, the theory of wavelets, and in mathematical and theoretical physics. Nine up-to-date contributions have been written on invitation by experts in the respective fields. The book is the third volume of the subseries "Advances in Partial Differential Equations".

Spectral Theory And Partial Differential Equations

Author: James V Ralston
Publisher: American Mathematical Soc.
ISBN: 1470409895
Size: 76.83 MB
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This volume contains the proceedings of the Conference on Spectral Theory and Partial Differential Equations, held from June 17-21, 2013, at the University of California, Los Angeles, California, in honor of James Ralston's 70th Birthday. Papers in this volume cover important topics in spectral theory and partial differential equations such as inverse problems, both analytical and algebraic; minimal partitions and Pleijel's Theorem; spectral theory for a model in Quantum Field Theory; and beams on Zoll manifolds.

Partial Differential Equations Vii

Author: M.A. Shubin
Publisher: Springer Science & Business Media
ISBN: 3662067196
Size: 63.97 MB
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This EMS volume contains a survey of the principles and advanced techniques of the spectral theory of linear differential and pseudodifferential operators in finite-dimensional spaces. Also including a special section of Sunada's recent solution of Kac's celebrated problem of whether or not "one can hear the shape of a drum".

Partial Differential Equations V

Author: M.V. Fedoryuk
Publisher: Springer
ISBN: 9783540533719
Size: 69.57 MB
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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.

Spectral And Scattering Theory For Second Order Partial Differential Operators

Author: Kiyoshi Mochizuki
Publisher: CRC Press
ISBN: 1351648942
Size: 68.96 MB
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The book is intended for students of graduate and postgraduate level, researchers in mathematical sciences as well as those who want to apply the spectral theory of second order differential operators in exterior domains to their own field. In the first half of this book, the classical results of spectral and scattering theory: the selfadjointness, essential spectrum, absolute continuity of the continuous spectrum, spectral representations, short-range and long-range scattering are summarized. In the second half, recent results: scattering of Schrodinger operators on a star graph, uniform resolvent estimates, smoothing properties and Strichartz estimates, and some applications are discussed.

Seminar On Singularities Of Solutions Of Linear Partial Differential Equations

Author: George F. Oster
Publisher: Princeton University Press
ISBN: 9780691082134
Size: 43.44 MB
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Singularities of solutions of differential equations forms the common theme of these papers taken from a seminar held at the Institute for Advanced Study in Princeton in 1977-1978. While some of the lectures were devoted to the analysis of singularities, others focused on applications in spectral theory. As an introduction to the subject, this volume treats current research in the field in such a way that it can be studied with profit by the non-specialist.

Spectral Theory And Differential Operators

Author: E. Brian Davies
Publisher: Cambridge University Press
ISBN: 9780521587105
Size: 28.13 MB
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In this book, Davies introduces the reader to the theory of partial differential operators, up to the spectral theorem for bounded linear operators on Banach spaces. He also describes the theory of Fourier transforms and distributions as far as is needed to analyze the spectrum of any constant coefficient partial differential operator. He also presents a completely new proof of the spectral theorem for unbounded self-adjoint operators and demonstrates its application to a variety of second order elliptic differential operators. Finally, the book contains a detailed account of the application of variational methods to estimate the eigenvalues of operators with measurable coefficients defined by the use of quadratic form techniques. Illustrated with many examples, it is well-suited to graduate-level work.

The Spectral Theory Of Periodic Differential Equations

Author: Michael Stephen Patrick Eastham
Size: 52.53 MB
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Suitable for advanced undergraduates and graduate students, this text surveys the classical theory of the calculus of variations. Topics include static systems, control systems, additional constraints, the Hamilton-Jacobi equation, and the accessory optimization problem. Emphasis throughout the text is placed upon methods and principles, which are illustrated by worked problems and sets of exercises. 1975 edition.