Shock Waves and Reaction—Diffusion Equations
Auteur : Joel Smoller
Éditeur : Springer Science & Business Media
Catégories : Mathematics, Mathematical Analysis, Mathematics, Calculus
Fiche de l'ebook
ISBN : 1461208734, isbn2
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.
Langue : 
EN
Date de sortie : 06/12/2012
Nombre de pages : 550
Type : Ebook
Nombre de fichier(s) : 1
Poids Total : 4.82 Mo
fr