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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)
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Front Matter
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Basic Linear Theory
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Front Matter
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Reaction-Diffusion Equations
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Front Matter
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The Theory of Shock Waves
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Front Matter
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Authors and Affiliations
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
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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