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Shock Waves and Reaction—Diffusion Equations

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  • © 1994
  • Latest edition

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Part of the book series: Grundlehren der mathematischen Wissenschaften (GL, volume 258)

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About this book

For this edition, a number of typographical errors and minor slip-ups have been corrected. In addition, following the persistent encouragement of Olga Oleinik, I have added a new chapter, Chapter 25, which I titled "Recent Results." This chapter is divided into four sections, and in these I have discussed what I consider to be some of the important developments which have come about since the writing of the first edition. Section I deals with reaction-diffusion equations, and in it are described both the work of C. Jones, on the stability of the travelling wave for the Fitz-Hugh-Nagumo equations, and symmetry-breaking bifurcations. Section II deals with some recent results in shock-wave theory. The main topics considered are L. Tartar's notion of compensated compactness, together with its application to pairs of conservation laws, and T.-P. Liu's work on the stability of viscous profiles for shock waves. In the next section, Conley's connection index and connection matrix are described; these general notions are useful in con­ structing travelling waves for systems of nonlinear equations. The final sec­ tion, Section IV, is devoted to the very recent results of C. Jones and R. Gardner, whereby they construct a general theory enabling them to locate the point spectrum of a wide class of linear operators which arise in stability problems for travelling waves. Their theory is general enough to be applica­ ble to many interesting reaction-diffusion systems.

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Keywords

Table of contents (25 chapters)

  1. The Theory of Shock Waves

  2. The Conley Index

Authors and Affiliations

  • Department of Mathematics, University of Michigan, Ann Arbor, USA

    Joel Smoller

Bibliographic Information

  • Book Title: Shock Waves and Reaction—Diffusion Equations

  • Authors: Joel Smoller

  • Series Title: Grundlehren der mathematischen Wissenschaften

  • DOI: https://doi.org/10.1007/978-1-4612-0873-0

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Science+Business Media New York 1994

  • Hardcover ISBN: 978-0-387-94259-9Published: 14 October 1994

  • Softcover ISBN: 978-1-4612-6929-8Published: 08 October 2012

  • eBook ISBN: 978-1-4612-0873-0Published: 06 December 2012

  • Series ISSN: 0072-7830

  • Series E-ISSN: 2196-9701

  • Edition Number: 2

  • Number of Pages: XXIII, 634

  • Topics: Analysis

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