Shock Waves and Reaction--Diffusion Equations

Smoller, Joel

  • 出版商: Springer
  • 出版日期: 2012-10-08
  • 售價: $10,030
  • 貴賓價: 9.5$9,529
  • 語言: 英文
  • 頁數: 634
  • 裝訂: Quality Paper - also called trade paper
  • ISBN: 1461269296
  • ISBN-13: 9781461269298
  • 相關分類: 工程數學 Engineering-mathematics物理學 Physics
  • 海外代購書籍(需單獨結帳)

商品描述

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.