Free And Moving Boundaries

Addressing algebraic problems found in biomathematics and energy, Free and Moving Boundaries: Analysis, Simulation and Control discusses moving boundary and boundary control in systems described by partial differential equations (PDEs). With contributions from international experts, the book emphasizes numerical and theoretical control of mo

Here is a wide-ranging, comprehensive account of the mathematical formulation of problems involving free boundaries as they occur in such diverse areas as hydrology, metallurgy, chemical engineering, soil science, molecular biology, materials science, and steel and glass production. Many newmethods of solution are discussed, including modern computer techniques which address multidimensional, multiphase practical problems.

Free boundary problems arise in an enormous number of situations in nature and technology. They hold a strategic position in pure and applied sciences and thus have been the focus of considerable research over the last three decades. Free Boundary Problems: Theory and Applications presents the work and results of experts at the forefront of current research in mathematics, material sciences, chemical engineering, biology, and physics. It contains the plenary lectures and contributed papers of the 1997 International Interdisciplinary Congress proceedings held in Crete. The main topics addressed include free boundary problems in fluid and solid mechanics, combustion, the theory of filtration, and glaciology. Contributors also discuss material science modeling, recent mathematical developments, and numerical analysis advances within their presentations of more specific topics, such as singularities of interfaces, cusp cavitation and fracture, capillary fluid dynamics of film coating, dynamics of surface growth, phase transition kinetics, and phase field models. With the implications of free boundary problems so far reaching, it becomes important for researchers from all of these fields to stay abreast of new developments. Free Boundary Problems: Theory and Applications provides the opportunity to do just that, presenting recent advances from more than 50 researchers at the frontiers of science, mathematics, and technology.

We hope that the tools and ideas presented here will serve as a basis for the study of more complex phenomena and problems."--Jacket.

Many phenomena of interest for applications are represented by differential equations which are defined in a domain whose boundary is a priori unknown, and is accordingly named a "free boundary". A further quantitative condition is then provided in order to exclude indeterminacy. Free boundary problems thus encompass a broad spectrum which is represented in this state-of-the-art volume by a variety of contributions of researchers in mathematics and applied fields like physics, biology and material sciences. Special emphasis has been reserved for mathematical modelling and for the formulation of new problems.

This text describes several computational techniques that can be applied to a variety of problems in thermo-fluid physics, multi-phase flow, and applied mechanics involving moving flow boundaries. Step-by-step discussions of numerical procedures include multiple examples that employ algorithms in problem-solving. In addition to its survey of contemporary numerical techniques, this volume discusses formulation and computation strategies as well as applications in many fields. Researchers and professionals in aerospace, chemical, mechanical, and materials engineering will find it a valuable resource. It is also an appropriate textbook for advanced courses in fluid dynamics, computation fluid dynamics, heat transfer, and numerical methods.