Handbook of Differential Equations: Evolutionary Equations - 1st Edition - ISBN: 9780444532220, 9780080932590

Handbook of Differential Equations: Evolutionary Equations, Volume 5

1st Edition

Editors: C.M. Dafermos Milan Pokorny
eBook ISBN: 9780080932590
Hardcover ISBN: 9780444532220
Imprint: North Holland
Published Date: 29th May 2009
Page Count: 534
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Table of Contents


List of Contributors

Contents of Volume I

Contents of Volume IIi

Contents of Volume III

Contents of Volume IV

1. Shallow-Water Equations and Related Topics

2. Fast Reaction Limit of Competition-Diffusion Systems

3. The Mathematics of Nonlinear Optics

4. Thermoelasticity

5. Unique Continuation Properties and Quantitative Estimates of Unique Continuation for Parabolic Equations

Author Index

Subject Index


Handbook of Differential Equations: Evolutionary Equations is the last text of a five-volume reference in mathematics and methodology. This volume follows the format set by the preceding volumes, presenting numerous contributions that reflect the nature of the area of evolutionary partial differential equations.

The book is comprised of five chapters that feature the following:

• A thorough discussion of the shallow-equations theory, which is used as a model for water waves in rivers, lakes and oceans. It covers the issues of modeling, analysis and applications. • Evaluation of the singular limits of reaction-diffusion systems, where the reaction is fast compared to the other processes; and applications that range from the theory of the evolution of certain biological processes to the phenomena of Turing and cross-diffusion instability • Detailed discussion of numerous problems arising from nonlinear optics, at the high-frequency and high-intensity regime • Geometric and diffractive optics, including wave interactions • Presentation of the issues of existence, blow-up and asymptotic stability of solutions, from the equations of solutions to the equations of linear and non-linear thermoelasticity • Answers to questions about unique space, such as continuation and backward uniqueness for linear second-order parabolic equations.

Research mathematicians, mathematics lecturers and instructors, and academic students will find this book invaluable.

Key Features

  • Review of new results in the area
  • Continuation of previous volumes in the handbook series covering evolutionary PDEs
  • New content coverage of DE applications


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North Holland
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About the Editors

C.M. Dafermos Editor

Affiliations and Expertise

Brown University, Providence, RI, USA

Milan Pokorny Editor

Affiliations and Expertise

Mathematical Institute, Charles University, Praha, Czech Republic