Grundlehren der mathematischen Wissenschaften

Shock Waves and Reaction—Diffusion Equations

Authors: Smoller, Joel

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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.

Table of contents (25 chapters)

Table of contents (25 chapters)

Buy this book

eBook $129.00
price for USA in USD
  • ISBN 978-1-4612-0873-0
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • Immediate eBook download after purchase and usable on all devices
  • Bulk discounts available
Hardcover $219.99
price for USA in USD
Softcover $169.99
price for USA in USD
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Bibliographic Information

Bibliographic Information
Book Title
Shock Waves and Reaction—Diffusion Equations
Authors
Series Title
Grundlehren der mathematischen Wissenschaften
Series Volume
258
Copyright
1994
Publisher
Springer-Verlag New York
Copyright Holder
Springer Science+Business Media New York
eBook ISBN
978-1-4612-0873-0
DOI
10.1007/978-1-4612-0873-0
Hardcover ISBN
978-0-387-94259-9
Softcover ISBN
978-1-4612-6929-8
Series ISSN
0072-7830
Edition Number
2
Number of Pages
XXIII, 634
Topics