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Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Vector & tensor analysis
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Shock Waves and Reaction-Diffusion Equations (Hardcover, 2nd ed. 1994)
Loot Price: R6,701
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Shock Waves and Reaction-Diffusion Equations (Hardcover, 2nd ed. 1994)
Series: Grundlehren der mathematischen Wissenschaften, 258
Expected to ship within 10 - 15 working days
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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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