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Author: James M. Hill
Publisher: Longman Scientific and Technical
ISBN:
Category : Mathematics
Languages : en
Pages : 232
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Book Description
Author: James M. Hill
Publisher: Longman Scientific and Technical
ISBN:
Category : Mathematics
Languages : en
Pages : 232
Get Book Here
Book Description
Author: N.L. Gol'dman
Publisher: Springer Science & Business Media
ISBN: 9401154880
Category : Mathematics
Languages : en
Pages : 264
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Book Description
In this monograph the theory and methods of solving inverse Stefan problems for quasilinear parabolic equations in regions with free boundaries are developed. The study of this new class of ill-posed problems is motivated by the needs of the mod eling and control of nonlinear processes with phase transitions in thermophysics and mechanics of continuous media. Inverse Stefan problems are important for the perfection of technologies both in high temperature processes (e.g., metallurgy, the aircraft industry, astronautics and power engineering) and in hydrology, exploitation of oil-gas fields, etc. The proposed book will complete a gap in these subjects in the preceding re searches of ill-posed problems. It contains the new theoretical and applied studies of a wide class of inverse Stefan problems. The statements of such problems on the determination of boundary functions and coefficients of the equation are considered for different types of additional information about their solution. The variational method of obtaining stable approximate solutions is proposed and established. It is implemented by an efficient computational scheme of descriptive regularization. This algorithm utilizes a priori knowledge of the qualitative structure of the sought solution and ensures a substantial saving in computational costs. It is tested on model and applied problems in nonlinear thermophysics. In particular, the results of calculations for important applications in continuous casting of ingots and in the melting of a plate with the help of laser technology are presented.
Author: S.C. Gupta
Publisher: Elsevier
ISBN: 008052916X
Category : Science
Languages : en
Pages : 404
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Book Description
This volume emphasises studies related to classical Stefan problems. The term "Stefan problem" is generally used for heat transfer problems with phase-changes such as from the liquid to the solid. Stefan problems have some characteristics that are typical of them, but certain problems arising in fields such as mathematical physics and engineering also exhibit characteristics similar to them. The term ``classical" distinguishes the formulation of these problems from their weak formulation, in which the solution need not possess classical derivatives. Under suitable assumptions, a weak solution could be as good as a classical solution. In hyperbolic Stefan problems, the characteristic features of Stefan problems are present but unlike in Stefan problems, discontinuous solutions are allowed because of the hyperbolic nature of the heat equation. The numerical solutions of inverse Stefan problems, and the analysis of direct Stefan problems are so integrated that it is difficult to discuss one without referring to the other. So no strict line of demarcation can be identified between a classical Stefan problem and other similar problems. On the other hand, including every related problem in the domain of classical Stefan problem would require several volumes for their description. A suitable compromise has to be made. The basic concepts, modelling, and analysis of the classical Stefan problems have been extensively investigated and there seems to be a need to report the results at one place. This book attempts to answer that need.
Author: L. I. Rubinšteĭn
Publisher: American Mathematical Soc.
ISBN: 1470428504
Category : Mathematics
Languages : en
Pages : 429
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Book Description
Translations of Mathematical Monographs
Author: A.M. Meirmanov
Publisher: Walter de Gruyter
ISBN: 3110846721
Category : Mathematics
Languages : en
Pages : 257
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Book Description
The aim of the series is to present new and important developments in pure and applied mathematics. Well established in the community over two decades, it offers a large library of mathematics including several important classics. The volumes supply thorough and detailed expositions of the methods and ideas essential to the topics in question. In addition, they convey their relationships to other parts of mathematics. The series is addressed to advanced readers wishing to thoroughly study the topic. Editorial Board Lev Birbrair, Universidade Federal do Ceará, Fortaleza, Brasil Victor P. Maslov, Russian Academy of Sciences, Moscow, Russia Walter D. Neumann, Columbia University, New York, USA Markus J. Pflaum, University of Colorado, Boulder, USA Dierk Schleicher, Jacobs University, Bremen, Germany
Author: Giuseppe Buttazzo
Publisher: Oxford University Press
ISBN: 9780198504658
Category : Mathematics
Languages : en
Pages : 282
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Book Description
While easier to solve and accessible to a broader range of students, one-dimensional variational problems and their associated differential equations exhibit many of the same complex behavior of higher-dimensional problems. This book, the first moden introduction, emphasizes direct methods and provides an exceptionally clear view of the underlying theory.
Author: John Rozier Cannon
Publisher: Cambridge University Press
ISBN: 9780521302432
Category : Mathematics
Languages : en
Pages : 522
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Book Description
This is a version of Gevrey's classical treatise on the heat equations. Included in this volume are discussions of initial and/or boundary value problems, numerical methods, free boundary problems and parameter determination problems. The material is presented as a monograph and/or information source book. After the first six chapters of standard classical material, each chapter is written as a self-contained unit except for an occasional reference to elementary definitions, theorems and lemmas in previous chapters.
Author: V. Alexiades
Publisher: CRC Press
ISBN: 9781560321255
Category : Science
Languages : en
Pages : 342
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Book Description
Presents mathematical models of melting and solidification processes that are the key to the effective performance of latent heat thermal energy storage systems, utilized in a wide range of heat transfer and industrial applications.
Author: Daniel V. Schroeder
Publisher:
ISBN: 0192895540
Category : Science
Languages : en
Pages : 435
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Book Description
This is a textbook for the standard undergraduate-level course in thermal physics (sometimes called thermodynamics or statistical mechanics). Originally published in 1999, it quickly gained market share and has now been the most widely used English-language text for such courses, as taught in physics departments, for more than a decade. Its clear and accessible writing style has also made it popular among graduate students and professionals who want to gain abetter understanding of thermal physics. The book explores applications to engineering, chemistry, biology, geology, atmospheric science, astrophysics, cosmology, and everyday life. It includes twoappendices, reference data, an annotated bibliography, a complete index, and 486 homework problems.
Author: Sanjoy Mahajan
Publisher: MIT Press
ISBN: 0262265591
Category : Education
Languages : en
Pages : 152
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Book Description
An antidote to mathematical rigor mortis, teaching how to guess answers without needing a proof or an exact calculation. In problem solving, as in street fighting, rules are for fools: do whatever works—don't just stand there! Yet we often fear an unjustified leap even though it may land us on a correct result. Traditional mathematics teaching is largely about solving exactly stated problems exactly, yet life often hands us partly defined problems needing only moderately accurate solutions. This engaging book is an antidote to the rigor mortis brought on by too much mathematical rigor, teaching us how to guess answers without needing a proof or an exact calculation. In Street-Fighting Mathematics, Sanjoy Mahajan builds, sharpens, and demonstrates tools for educated guessing and down-and-dirty, opportunistic problem solving across diverse fields of knowledge—from mathematics to management. Mahajan describes six tools: dimensional analysis, easy cases, lumping, picture proofs, successive approximation, and reasoning by analogy. Illustrating each tool with numerous examples, he carefully separates the tool—the general principle—from the particular application so that the reader can most easily grasp the tool itself to use on problems of particular interest. Street-Fighting Mathematics grew out of a short course taught by the author at MIT for students ranging from first-year undergraduates to graduate students ready for careers in physics, mathematics, management, electrical engineering, computer science, and biology. They benefited from an approach that avoided rigor and taught them how to use mathematics to solve real problems. Street-Fighting Mathematics will appear in print and online under a Creative Commons Noncommercial Share Alike license.
