Evolution Equations in Scales of Banach Spaces (Teubner-Texte zur Mathematik 140) (2002. 309 p. 309 p. 2 illus. 240 mm)

Evolution Equations in Scales of Banach Spaces (Teubner-Texte zur Mathematik 140) (2002. 309 p. 309 p. 2 illus. 240 mm)

  • ただいまウェブストアではご注文を受け付けておりません。 ⇒古書を探す
  • 製本 Paperback:紙装版/ペーパーバック版
  • 言語 ENG
  • 商品コード 9783519003762
  • DDC分類 515

Full Description

The book provides a new functional-analytic approach to evolution equations by considering the abstract Cauchy problem in a scale of Banach spaces. Conditions are proved characterizing well-posedness of the linear, time-dependent Cauchy problem in scales of Banach spaces and implying local existence, uniqueness, and regularity of solutions of the quasilinear Cauchy problem. Many applications illustrate the generality of the approach. In particular, using the Fefferman-Phong inequality unifying results on parabolic and hyperbolic equations generalizing classical ones and a unified treatment of Navier-Stokes and Euler equations is described. Assuming only basic knowledge in analysis and functional analysis the book provides all mathematical tools and is aimed for students, graduates, researchers, and lecturers.

Contents

Tools from functional analysis - Well-posedness of the time-dependent linear Cauchy problem - Quasilinear evolution equations - Applications to linear, time-dependent evolution equations - Applications to quasilinear evolution equations