Inverse Problems for Fractional Partial Differential Equations (Graduate Studies in Mathematics, 230)

Science & Math

Rundell, William

Kaltenbacher, Barbara

Mathematics

Amer Mathematical Society

Nonlinear inverse problems appear in many applications, and typically they lead to mathematical models that are ill-posed, i.e., they are unstable under data perturbations. Those problems require a regularization, i.e., a special&nbsp; numerical treatment. This book presents regularization schemes which are based on iteration methods, e.g., nonlinear Landweber iteration, level set methods, multilevel methods and Newton type methods.

Iterative Regularization Methods for Nonlinear Ill-Posed Problems (Radon Series on Computational and Applied Mathematics, 6)

Scherzer, Otmar

Neubauer, Andreas

de Gruyter

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.

Mathematical Theory of Evolutionary Fluid-Flow Structure Interactions (Oberwolfach Seminars, 48)

Lasiecka, Irena

Triggiani, Roberto

Kukavica, Igor

Tuffaha, Amjad

Webster, Justin T.

Birkhauser

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