## Moving Interfaces and Quasilinear Parabolic Evolution EquationsIn 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 problems, one- and two-phase Stokes problems, and the equations of incompressible viscous one- and two-phase fluid flows. The theory of maximal regularity, an essential element, is also fully developed. The authors present a modern approach based on powerful tools in classical analysis, functional analysis, and vector-valued harmonic analysis. The theory is applied to problems in two-phase fluid dynamics and phase transitions, one-phase generalized Newtonian fluids, nematic liquid crystal flows, Maxwell-Stefan diffusion, and a variety of geometric evolution equations. The book also includes a discussion of the underlying physical and thermodynamic principles governing the equations of fluid flows and phase transitions, and an exposition of the geometry of moving hypersurfaces. |

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### Contents

3 | |

2
Tools from Differential Geometry | 43 |

Part II
Abstract Theory | 87 |

3
Operator Theory and Semigroups | 88 |

4
VectorValued Harmonic Analysis | 149 |

5
Quasilinear Parabolic Evolution Equations | 195 |

Part III
Linear Theory | 231 |

6
Elliptic and Parabolic Problems | 232 |

Part IV
Nonlinear Problems | 417 |

9
Local WellPosedness and Regularity | 418 |

10
Linear Stability of Equilibria | 451 |

11
Qualitative Behaviour of the Semiflows | 491 |

12
Further Parabolic Evolution Problems | 515 |

Bibliographical Comments | 571 |

Outlook and Future Challenges | 585 |

List of Figures | 587 |

### Other editions - View all

Moving Interfaces and Quasilinear Parabolic Evolution Equations Jan Prüss,Gieri Simonett No preview available - 2016 |