| Energy Methods for Free Boundary Problems: Applications to Nonlinear Pdes and Fluid Mechanics 2002 Edition Contributor(s): Antontsev, S. N. (Author), Diaz, J. I. (Author), Shmarev, S. (Author) |
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ISBN: 0817641238 ISBN-13: 9780817641238 Publisher: Birkhauser OUR PRICE: $161.49 Product Type: Hardcover - Other Formats Published: October 2001 Annotation: Presents an integrated account of modern developments in energy methods for studying free boundary problems in PDEs. The theory presented has particular relevance to a number of physical applications, including heat conduction, surface and underground water flow, filtration through porous media, flows of non-Newtonian fluids, boundary layers, chemical reactions, and semiconductors. The work is divided into two parts: An exposition of the methods of several general classes of nonlinear equations and systems and applications to the theory. Of interest to applied mathematicians and graduate students whose research is in partial differential equations, nonlinear analysis, and continuum mechanics. Applications to a number of different problems arising in continuum mechanics (fluid dynamics) are presented making this book of equal interest to physicists and engineers. |
| Additional Information |
| BISAC Categories: - Mathematics | Differential Equations - Partial - Mathematics | Applied - Medical |
| Dewey: 515.353 |
| LCCN: 2001052680 |
| Series: Progress in Nonlinear Differential Equations and Their Applications |
| Physical Information: 0.9" H x 6.39" W x 9.48" (1.42 lbs) 332 pages |
| Descriptions, Reviews, Etc. |
| Publisher Description: For the past several decades, the study of free boundary problems has been a very active subject of research occurring in a variety of applied sciences. What these problems have in common is their formulation in terms of suitably posed initial and boundary value problems for nonlinear partial differential equations. Such problems arise, for example, in the mathematical treatment of the processes of heat conduction, filtration through porous media, flows of non-Newtonian fluids, boundary layers, chemical reactions, semiconductors, and so on. The growing interest in these problems is reflected by the series of meetings held under the title "Free Boundary Problems: Theory and Applications" (Ox- ford 1974, Pavia 1979, Durham 1978, Montecatini 1981, Maubuisson 1984, Irsee 1987, Montreal 1990, Toledo 1993, Zakopane 1995, Crete 1997, Chiba 1999). From the proceedings of these meetings, we can learn about the different kinds of mathematical areas that fall within the scope of free boundary problems. It is worth mentioning that the European Science Foundation supported a vast research project on free boundary problems from 1993 until 1999. The recent creation of the specialized journal Interfaces and Free Boundaries: Modeling, Analysis and Computation gives us an idea of the vitality of the subject and its present state of development. This book is a result of collaboration among the authors over the last 15 years. |