Moving interfaces and quasilinear parabolic evolution equations / by Jan Prüss, Gieri Simonett.

Format:

Book

Author/Creator:

Prüss, Jan., Author.

Simonett, Gieri., Author.

Series:

Monographs in Mathematics, 1017-0480 ; 105

Language:

English

Subjects (All):

Differential equations, Partial.

Physics.

Functional analysis.

Partial Differential Equations.

Mathematical Methods in Physics.

Functional Analysis.

Local Subjects:

Partial Differential Equations.

Mathematical Methods in Physics.

Functional Analysis.

Physical Description:

1 online resource (XIX, 609 p. 7 illus.)

Edition:

1st ed. 2016.

Place of Publication:

Cham : Springer International Publishing : Imprint: Birkhäuser, 2016.

Summary:

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 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.

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.

Notes:

Includes bibliographical references and index.

ISBN:

3-319-27698-0