Distributions in the physical and engineering sciences Volume 2 Linear and nonlinear dynamics in continuous media Alexander I. Saichev, Wojbor A. Woyczynski

Format:

Book

Author/Creator:

Saichev, A. I., author.

Woyczyński, W. A. (Wojbor Andrzej), 1943- author.

Series:

Applied and numerical harmonic analysis

Language:

English

Subjects (All):

Differential equations, Partial.

Differential equations, Linear.

Engineering mathematics.

Physical Description:

1 online resource

Other Title:

Linear and nonlinear dynamics in continuous media

Place of Publication:

New York Birkhäuser 2013

System Details:

text file

PDF

Summary:

Distributions in the Physical and Engineering Sciences is a comprehensive exposition on analytic methods for solving science and engineering problems. It is written from the unifying viewpoint of distribution theory and enriched with many modern topics that are important for practitioners and researchers. The goal of the books is to give the reader, specialist and non-specialist, useable and modern mathematical tools in their research and analysis. Volume 2: Linear and Nonlinear Dynamics of Continuous Media continues the multivolume project that endeavors to show how the theory of distributions, also called the theory of generalized functions, can be used by graduate students and researchers in applied mathematics, physical sciences, and engineering. It contains an analysis of the three basic types of linear partial differential equationselliptic, parabolic, and hyperbolicas well as chapters on first-order nonlinear partial differential equations and conservation laws, and generalized solutions of first-order nonlinear PDEs. Nonlinear wave, growing interface, and Burgers equations, KdV equations, and the equations of gas dynamics and porous media are also covered. The careful explanations, accessible writing style, many illustrations/examples and solutions also make it suitable for use as a self-study reference by anyone seeking greater understanding and proficiency in the problem solving methods presented. The book is ideal for a general scientific and engineering audience, yet it is mathematically precise. Features Application oriented exposition of distributional (Dirac delta) methods in the theory of partial differential equations. Abstract formalism is keep to a minimum. Careful and rich selection of examples and problems arising in real-life situations. Complete solutions to all exercises appear at the end of the book. Clear explanations, motivations, and illustration of all necessary mathematical concepts

Contents:

Potential Theory and Fundamental Solutions of Elliptic Equations Diffusions and Parabolic Evolution Equations Waves and Hyperbolic Equations First Order Nonlinear PDEs and Conservation Laws Generalized Solutions of First Order Nonlinear PDEs Nonlinear waves and growing interfaces: 1-D Burgers-KPZ models Other Standard Nonlinear Models of Higher Order

Appendix A: Answers and Solutions

Appendix B: Bibliographical Notes

Notes:

Includes bibliographical references and index

Print version record

Other Format:

Print version Saichev, A.I. Distributions in the physical and engineering sciences. Volume 2, Linear and nonlinear dynamics in continuous media

ISBN:

9780817646523

0817646523

081763942X

9780817639426

OCLC:

858278569

Access Restriction:

Restricted for use by site license