Birkhauser Moving Interfaces and Quasilinear Parabolic Equations

This monograph from Birkhauser offers a deep mathematical analysis for researchers and students focused on moving interface problems. The text provides a detailed study of abstract quasilinear parabolic evolution equations, covering essential topics such as elliptic and parabolic boundary value problems and transmission problems. Readers will find a thorough examination of one- and two-phase Stokes problems, alongside the equations governing incompressible viscous one- and two-phase fluid flows. A significant portion of the work is dedicated to the theory of maximal regularity, which serves as a fundamental element of the mathematical framework presented. Using modern tools from classical analysis, the authors provide a structured approach to solving complex problems in mathematical analysis and differential equations. This volume is a specialized resource for those studying the mathematical foundations of fluid flows and evolution equations.