Mathematical Theory of Evolutionary Fluid-Flow Structure Interactions

This book is devoted to the study of coupled partial differential equation models, which describe complex dynamical systems occurring in modern scientific applications such as fluid/flow-structure interactions. The first chapter provides a general description of a fluid-structure interaction, which is formulated within a realistic framework, where the structure subject to a frictional damping moves within the fluid. The second chapter then offers a multifaceted description, with often surprising results, of the case of the static interface; a case that is argued in the literature to be a good model for small, rapid oscillations of the structure. The third chapter describes flow-structure interaction where the compressible Navier-Stokes equations are replaced by the linearized Euler equation, while the solid is taken as a nonlinear plate, which oscillates in the surrounding gas flow. The final chapter focuses on a the equations of nonlinear acoustics coupled with linear acousticsor elasticity, as they arise in the context of high intensity ultrasound applications.

Describes in a user-friendly way recent advances in mathematical analysis of coupled PDE-systems with interaction at the interface Indicates attractive directions for future research, including several open problems Presents PhD students an excellent starting point for their own research in the area

Auteur
Barbara Kaltenbacher

Igor Kukavica

Irena Lasiecka

Roberto Triggiani

Amjad Tuffaha

Justin T. Webster

Contenu
An introduction to a fluid-structure model.- Linear parabolic-hyperbolic fluid-structure interaction models.- Flow-plate interactions: well-posedness and long-time behavior.- Some aspects in nonlinear acoustics coupling and shape optimization