Moving Interfaces and Quasilinear Parabolic Evolution Equations

• Main Authors: Prüss, Jan (Author), Simonett, Gieri (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Cham : Springer International Publishing : Imprint: Birkhäuser, 2016.
• Series: Monographs in Mathematics, 105
• Subjects: Mathematics.; Functional analysis.; Partial differential equations.; Physics.; Partial Differential Equations.; Mathematical Methods in Physics.; Functional Analysis.

In this monograph, the authors develop a comprehensive approach for the mathematical analysis of a wide array of problems involving moving interfaces. It includes an in-depth study of abstract quasilinear parabolic evolution equations, elliptic and parabolic boundary value problems, transmission pro...

Table of Contents:

• Preface
• Basic Notations
• General References
• Part I Background
• 1Problems and Strategies
• 2.Tools from Differential Geometry
• Part II Abstract Theory
• 3Operator Theory and Semigroups
• 4.Vector-Valued Harmonic Analysis
• 5.Quasilinear Parabolic Evolution Equations
• Part III Linear Theory
• 6.Elliptic and Parabolic Problems
• 7.Generalized Stokes Problems
• 8.Two-Phase Stokes Problems
• Part IV Nonlinear Problems
• 9.Local Well-Posedness and Regularity
• 10.Linear Stability of Equilibria
• 11.Qualitative Behaviour of the Semiows
• 12.Further Parabolic Evolution Problems
• Biographical Comments
• Outlook and Future Challenges
• References
• List of Figures
• List of Symbols
• Subject Index.