Some Applications of Functional Analysis in Mathematical Physics

Author: Sergeĭ Lʹvovich Sobolev

Publisher: American Mathematical Soc.

ISBN:

Category: Mathematics

Page: 286

View: 979

Translation of the 1988 Russian exposition of the theory of the function spaces now called Sobolev spaces, which are widely used in the theory of partial differential equations, mathematical physics, and numerous applications; of the variational method of solution of boundary value problems for elli"

Some Applications of Functional Analysis in Mathematical Physics

Author: S. L. Sobolev

Publisher: American Mathematical Soc.

ISBN:

Category:

Page: 286

View: 529

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

Applied Functional Analysis

Applications to Mathematical Physics

Author: Eberhard Zeidler

Publisher: Springer Science & Business Media

ISBN:

Category: Mathematics

Page: 481

View: 632

The first part of a self-contained, elementary textbook, combining linear functional analysis, nonlinear functional analysis, numerical functional analysis, and their substantial applications with each other. As such, the book addresses undergraduate students and beginning graduate students of mathematics, physics, and engineering who want to learn how functional analysis elegantly solves mathematical problems which relate to our real world. Applications concern ordinary and partial differential equations, the method of finite elements, integral equations, special functions, both the Schroedinger approach and the Feynman approach to quantum physics, and quantum statistics. As a prerequisite, readers should be familiar with some basic facts of calculus. The second part has been published under the title, Applied Functional Analysis: Main Principles and Their Applications.

Elements of the Theory of Functions and Functional Analysis

Author: Andre? Nikolaevich Kolmogorov

Publisher: Courier Corporation

ISBN:

Category: Mathematics

Page: 288

View: 552

Advanced-level text, now available in a single volume, discusses metric and normed spaces, continuous curves in metric spaces, measure theory, Lebesque intervals, Hilbert space, more. Exercises. 1957 edition.

Methods of Modern Mathematical Physics: Functional analysis

Author: Michael Reed

Publisher: Gulf Professional Publishing

ISBN:

Category: Science

Page: 400

View: 674

This book is the first of a multivolume series devoted to an exposition of functional analysis methods in modern mathematical physics. It describes the fundamental principles of functional analysis and is essentially self-contained, although there are occasional references to later volumes. We have included a few applications when we thought that they would provide motivation for the reader. Later volumes describe various advanced topics in functional analysis and give numerous applications in classical physics, modern physics, and partial differential equations.

Functional Analysis in Mechanics

Author: Leonid P. Lebedev

Publisher: Springer Science & Business Media

ISBN:

Category: Mathematics

Page: 244

View: 453

This is a self-contained book that covers the foundations of functional analysis while introducing the essential topics of the chosen applications. Graduate level students in mathematics and engineering will find the text useful.

Nonlinear Theory of Shallow Shells

Author: Iosif I. Vorovich

Publisher: Springer Science & Business Media

ISBN:

Category: Technology & Engineering

Page: 390

View: 579

This book presents rigorous treatment of boundary value problems in nonlinear theory of shallow shells. The consideration of the problems is carried out using methods of nonlinear functional analysis.

Qualitative theory of parabolic equations. 1

Author: Tadeĭ Ivanovich Zeleni︠a︡k

Publisher: VSP

ISBN:

Category: Mathematics

Page: 417

View: 857

In the qualitative theory of ordinary differential equations, the Liapunov method plays a fundamental role. To use their analogs for the analysis of stability of solutions to parabolic, hyperparabolic, and other nonclassical equations and systems, time-invariant a priori estimates have to be devised for solutions. In this publication only parabolic problems are considered. Here lie, mainly, the problems which have been investigated most thoroughly --- the construction of Liapunov functionals which naturally generalize Liapunov functions for nonlinear parabolic equations of the second order with one spatial variable. The authors establish stabilizing solutions theorems, and the necessary and sufficient conditions of general and asymptotic stability of stationary solutions, including the so-called critical case. Attraction domains for stable solutions of mixed problems for these equations are described. Furthermore, estimates for the number of stationary solutions are obtained.

Some Asymptotic Problems in the Theory of Partial Differential Equations

Author: Olga Oleinik

Publisher: Cambridge University Press

ISBN:

Category: Mathematics

Page: 202

View: 208

In this book, Professor Oleinik highlights her work in the area of partial differential equations. The book is divided into two parts: the first is devoted to the study of the asymptotic behavior at infinity of solutions of a class of nonlinear second order elliptic equations in unbounded and, in particular, cylindrical domains. The second contains the most recent results of the author in the theory of homogenization of partial differential equations and is concerned with questions about partially perforated domains and of solutions with rapidly alternating types of boundary conditions. Many of the results here have not appeared in book form before, and it sheds new light on the subject, raising many new ideas and open problems.