Mathematical Theory of Evolutionary Fluid-Flow Structure Interactions

1. Front Matter

   Pages i-xiii

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2. An introduction to a fluid-structure model

   • Igor Kukavica, Amjad Tuffaha

   Pages 1-52

3. Linear parabolic-hyperbolic fluid-structure interaction models. The case of static interface

   • Roberto Triggiani

   Pages 53-171

4. Flow-plate interactions: well-posedness and long time behavior

   • Irena Lasiecka, Justin T. Webster

   Pages 173-268

5. Some aspects in nonlinear acoustics: structure-acoustic coupling and shape optimization

   • Barbara Kaltenbacher

   Pages 269-307

6. Correction to: Mathematical Theory of Evolutionary Fluid-Flow Structure Interactions

   • Barbara Kaltenbacher, Igor Kukavica, Irena Lasiecka, Roberto Triggiani, Amjad Tuffaha, Justin T. Webster

   Pages E1-E1

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 acoustics or elasticity, as they arise in the context of high intensity ultrasound applications.

• fluid-structure interaction
• flow-structure interaction
• nonlinear structural acoustic interaction
• mathematical theory of evolutionary
• Oberwolfach
• partial differential equations

• Insitute of Mathematics, University of Klagenfurt, Klagenfurt am Wörthersee, Austria

  Barbara Kaltenbacher

• Department of Mathematics, University of Southern California, Los Angeles, USA

  Igor Kukavica

• Dept of Mathematical Sciences, University of Memphis, Memphis, USA

  Irena Lasiecka, Roberto Triggiani

• American University of Sharjah, Sharjah, United Arab Emirates

  Amjad Tuffaha

• Department of Mathematics and Statistics, University of Maryland, Baltimore County, Baltimore, USA

  Justin T. Webster

Barbara Kaltenbacher

Igor Kukavica

Irena Lasiecka

Roberto Triggiani

Amjad Tuffaha

Justin T. Webster