Evolution Equations in Scales of Banach Spaces
By: by Oliver Caps
Series: Teubner-Texte zur Mathematik, 0138-502X -- 140; Teubner-Texte zur Mathematik -- 140.
Publisher: Vieweg+Teubner Verlag
Published: 2002
Place of publication: Wiesbaden
Language: eng
Format: [electronic resource] /
Number of pages: 309
ISBN-13: 9783322800398
Subjects: Mathematics; Global analysis (Mathematics)
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.