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Author: J. I. Díaz Publisher: ISBN: Category : Boundary value problems Languages : en Pages : 344
Book Description
In this Research Note the author brings together the body of known work and presents many recent results relating to nonlinear partial differential equations that give rise to a free boundary--usually the boundary of the set where the solution vanishes identically. The formation of such a boundary depends on an adequate balance between two of the terms of the equation that represent the particular characteristics of the phenomenon under consideration: diffusion, absorption, convection, evolution etc. These balances do not occur in the case of a linear equation or an arbitrary nonlinear equation. Their characterization is studied for several classes of nonlinear equations relating to applications such as chemical reactions, non-Newtonian fluids, flow through porous media and biological populations. In this first volume, the free boundary for nonlinear elliptic equations is discussed. A second volume dealing with parabolic and hyperbolic equations is in preparation.
Author: J. I. Díaz Publisher: ISBN: Category : Boundary value problems Languages : en Pages : 344
Book Description
In this Research Note the author brings together the body of known work and presents many recent results relating to nonlinear partial differential equations that give rise to a free boundary--usually the boundary of the set where the solution vanishes identically. The formation of such a boundary depends on an adequate balance between two of the terms of the equation that represent the particular characteristics of the phenomenon under consideration: diffusion, absorption, convection, evolution etc. These balances do not occur in the case of a linear equation or an arbitrary nonlinear equation. Their characterization is studied for several classes of nonlinear equations relating to applications such as chemical reactions, non-Newtonian fluids, flow through porous media and biological populations. In this first volume, the free boundary for nonlinear elliptic equations is discussed. A second volume dealing with parabolic and hyperbolic equations is in preparation.
Author: S.N. Antontsev Publisher: Springer Science & Business Media ISBN: 9780817641238 Category : Technology & Engineering Languages : en Pages : 348
Book 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.
Author: Gui-Qiang Chen Publisher: American Mathematical Soc. ISBN: 0821835335 Category : Mathematics Languages : en Pages : 336
Book Description
The Emphasis Year on Nonlinear Partial Differential Equations and Related Analysis at Northwestern University produced this fine collection of original research and survey articles. Many well-known mathematicians attended the events and submitted their contributions for this volume. Eighteen papers comprise this work, representing the most significant advances and current trends in nonlinear PDEs and their applications. Topics covered include elliptic and parabolic equations, NavierStokes equations, and hyperbolic conservation laws. Important applications are presented from incompressible and compressible fluid mechanics, combustion, and electromagnetism. Also included are articles on recent advances in statistical reliability in modeling, simulation, level set methods forimage processing, shock waves, free boundaries, boundary layers, errors in numerical solutions, stability, instability, and singular limits. The volume is suitable for researchers and graduate students interested in partial differential equations.
Author: Isabel Narra Figueiredo Publisher: Springer Science & Business Media ISBN: 3764377194 Category : Mathematics Languages : en Pages : 462
Book Description
This book collects refereed lectures and communications presented at the Free Boundary Problems Conference (FBP2005). These discuss the mathematics of a broad class of models and problems involving nonlinear partial differential equations arising in physics, engineering, biology and finance. Among other topics, the talks considered free boundary problems in biomedicine, in porous media, in thermodynamic modeling, in fluid mechanics, in image processing, in financial mathematics or in computations for inter-scale problems.
Author: Robert Hardt Publisher: American Mathematical Soc. ISBN: 9780821804315 Category : Mathematics Languages : en Pages : 356
Book Description
This book contains lecture notes of minicourses at the Regional Geometry Institute at Park City, Utah, in July 1992. Presented here are surveys of breaking developments in a number of areas of nonlinear partial differential equations in differential geometry. The authors of the articles are not only excellent expositors, but are also leaders in this field of research. All of the articles provide in-depth treatment of the topics and require few prerequisites and less background than current research articles.
Author: J. I. Díaz
Author: J. I. Díaz
Author: S.N. Antontsev
Author: W. F. Ames
Author: H. Fujita
Author: Stanislav Nikolaevich Antont︠s︡ev
Author: DIAZ J.I.
Author: Gui-Qiang Chen
Author: Isabel Narra Figueiredo
Author: Robert Hardt
Author: J. I. Diaz