Shock Waves and Reaction-Diffusion Equations (Hardcover, 2nd ed. 1994)

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."

General

Imprint:	Springer-Verlag New York
Country of origin:	United States
Series:	Grundlehren der mathematischen Wissenschaften, 258
Release date:	October 1994
First published:	1994
Authors:	Joel Smoller
Dimensions:	235 x 155 x 34mm (L x W x T)
Format:	Hardcover
Pages:	634
Edition:	2nd ed. 1994
ISBN-13:	978-0-387-94259-9
Categories:	Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Vector & tensor analysis
LSN:	0-387-94259-9
Barcode:	9780387942599

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