Inverse Stefan Problems

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Inverse Stefan Problems

Author : N.L. Gol'dman
Publisher : Springer Science & Business Media
ISBN 13 : 9401154880
Total Pages : 264 pages
Book Rating : 4.4/5 (11 download)

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Book Synopsis Inverse Stefan Problems by : N.L. Gol'dman

Download or read book Inverse Stefan Problems written by N.L. Gol'dman and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

The Classical Stefan Problem

Author : S.C. Gupta
Publisher : Elsevier
ISBN 13 : 0444635823
Total Pages : 752 pages
Book Rating : 4.4/5 (446 download)

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Book Synopsis The Classical Stefan Problem by : S.C. Gupta

Download or read book The Classical Stefan Problem written by S.C. Gupta and published by Elsevier. This book was released on 2017-07-27 with total page 752 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Classical Stefan Problem: Basic Concepts, Modelling and Analysis with Quasi-Analytical Solutions and Methods, New Edition, provides the fundamental theory, concepts, modeling, and analysis of the physical, mathematical, thermodynamical, and metallurgical properties of classical Stefan and Stefan-like problems as applied to heat transfer problems with phase-changes, such as from liquid to solid. This self-contained work reports and derives the results from tensor analysis, differential geometry, non-equilibrium thermodynamics, physics, and functional analysis, and is thoroughly enriched with many appropriate references for in-depth background reading on theorems. Each chapter in this fully revised and updated edition begins with basic concepts and objectives, also including direction on how the subject matter was developed. It contains more than 400 pages of new material on quasi-analytical solutions and methods of classical Stefan and Stefan-like problems.The book aims to bridge the gap between the theoretical and solution aspects of the afore-mentioned problems. Provides both the phenomenology and mathematics of Stefan problems Bridges physics and mathematics in a concrete and readable manner Presents well-organized chapters that start with proper definitions followed by explanations and references for further reading Includes both numerical and quasi-analytical solutions and methods of classical Stefan and Stefan-like problems

The Classical Stefan Problem

Author : S.C. Gupta
Publisher : Elsevier
ISBN 13 : 008052916X
Total Pages : 404 pages
Book Rating : 4.0/5 (85 download)

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Book Synopsis The Classical Stefan Problem by : S.C. Gupta

Download or read book The Classical Stefan Problem written by S.C. Gupta and published by Elsevier. This book was released on 2003-10-22 with total page 404 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

An Inverse Stefan Problem

Author : Alun H. Williams
Publisher :
ISBN 13 :
Total Pages : 132 pages
Book Rating : 4.:/5 (654 download)

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Book Synopsis An Inverse Stefan Problem by : Alun H. Williams

Download or read book An Inverse Stefan Problem written by Alun H. Williams and published by . This book was released on 1989 with total page 132 pages. Available in PDF, EPUB and Kindle. Book excerpt:

The Stefan Problem

Author : L. I. Rubinšteĭn
Publisher : American Mathematical Soc.
ISBN 13 : 1470428504
Total Pages : 429 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis The Stefan Problem by : L. I. Rubinšteĭn

Download or read book The Stefan Problem written by L. I. Rubinšteĭn and published by American Mathematical Soc.. This book was released on 2000-01-25 with total page 429 pages. Available in PDF, EPUB and Kindle. Book excerpt: Translations of Mathematical Monographs

The Inverse Stefan Problem for the Heat Equation in Two Space Variables

Author : David L. Colton
Publisher :
ISBN 13 :
Total Pages : 12 pages
Book Rating : 4.:/5 (227 download)

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Book Synopsis The Inverse Stefan Problem for the Heat Equation in Two Space Variables by : David L. Colton

Download or read book The Inverse Stefan Problem for the Heat Equation in Two Space Variables written by David L. Colton and published by . This book was released on 1974 with total page 12 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper the author outlines an inverse method for constructing analytic solutions to the (single phase) Stefan problem for the heat equation in two space dimensions.

Solution of Inverse Stefan Problem Using a New Enthalpy Method

Author : Mulugeta K. Berhe
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (11 download)

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Book Synopsis Solution of Inverse Stefan Problem Using a New Enthalpy Method by : Mulugeta K. Berhe

Download or read book Solution of Inverse Stefan Problem Using a New Enthalpy Method written by Mulugeta K. Berhe and published by . This book was released on 1995 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

One-dimensional Stefan Problems

Author : James M. Hill
Publisher : Longman Scientific and Technical
ISBN 13 :
Total Pages : 232 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis One-dimensional Stefan Problems by : James M. Hill

Download or read book One-dimensional Stefan Problems written by James M. Hill and published by Longman Scientific and Technical. This book was released on 1987 with total page 232 pages. Available in PDF, EPUB and Kindle. Book excerpt:

The numerical solution of the inverse Stefan problem in two space variables

Author : David Colton
Publisher :
ISBN 13 :
Total Pages : 25 pages
Book Rating : 4.:/5 (256 download)

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Book Synopsis The numerical solution of the inverse Stefan problem in two space variables by : David Colton

Download or read book The numerical solution of the inverse Stefan problem in two space variables written by David Colton and published by . This book was released on 1983 with total page 25 pages. Available in PDF, EPUB and Kindle. Book excerpt:

A Method for the Numerical Solution of the One-dimensional Inverse Stefan Problem

Author : Rembert Reemtsen
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (83 download)

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Book Synopsis A Method for the Numerical Solution of the One-dimensional Inverse Stefan Problem by : Rembert Reemtsen

Download or read book A Method for the Numerical Solution of the One-dimensional Inverse Stefan Problem written by Rembert Reemtsen and published by . This book was released on 1982 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

The Stefan Problem

Author : A.M. Meirmanov
Publisher : Walter de Gruyter
ISBN 13 : 3110846721
Total Pages : 257 pages
Book Rating : 4.1/5 (18 download)

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Book Synopsis The Stefan Problem by : A.M. Meirmanov

Download or read book The Stefan Problem written by A.M. Meirmanov and published by Walter de Gruyter. This book was released on 2011-05-03 with total page 257 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Large Scale Inverse Problems

Author : Mike Cullen
Publisher : Walter de Gruyter
ISBN 13 : 3110282267
Total Pages : 216 pages
Book Rating : 4.1/5 (12 download)

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Book Synopsis Large Scale Inverse Problems by : Mike Cullen

Download or read book Large Scale Inverse Problems written by Mike Cullen and published by Walter de Gruyter. This book was released on 2013-08-29 with total page 216 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is thesecond volume of a three volume series recording the "Radon Special Semester 2011 on Multiscale Simulation & Analysis in Energy and the Environment" that took placein Linz, Austria, October 3-7, 2011. This volume addresses the common ground in the mathematical and computational procedures required for large-scale inverse problems and data assimilation in forefront applications. The solution of inverse problems is fundamental to a wide variety of applications such as weather forecasting, medical tomography, and oil exploration. Regularisation techniques are needed to ensure solutions of sufficient quality to be useful, and soundly theoretically based. This book addresses the common techniques required for all the applications, and is thus truly interdisciplinary. Thiscollection of surveyarticlesfocusses onthe large inverse problems commonly arising in simulation and forecasting in the earth sciences. For example, operational weather forecasting models have between 107 and 108 degrees of freedom. Even so, these degrees of freedom represent grossly space-time averaged properties of the atmosphere. Accurate forecasts require accurate initial conditions. With recent developments in satellite data, there are between 106 and 107 observations each day. However, while these also represent space-time averaged properties, the averaging implicit in the measurements is quite different from that used in the models. In atmosphere and ocean applications, there is a physically-based model available which can be used to regularise the problem. We assume that there is a set of observations with known error characteristics available over a period of time. The basic deterministic technique is to fit a model trajectory to the observations over a period of time to within the observation error. Since the model is not perfect the model trajectory has to be corrected, which defines the data assimilation problem. The stochastic view can be expressed by using an ensemble of model trajectories, and calculating corrections to both the mean value and the spread which allow the observations to be fitted by each ensemble member. In other areas of earth science, only the structure of the model formulation itself is known and the aim is to use the past observation history to determine the unknown model parameters. The book records the achievements of Workshop2 "Large-Scale Inverse Problems and Applications in the Earth Sciences". Itinvolves experts in the theory of inverse problems together with experts working on both theoretical and practical aspects of the techniques by which large inverse problems arise in the earth sciences.

A method for the numerical solution of the one-dimensional inverse Stefan problem

Author : 12 b82
Publisher :
ISBN 13 :
Total Pages : 21 pages
Book Rating : 4.:/5 (745 download)

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Book Synopsis A method for the numerical solution of the one-dimensional inverse Stefan problem by : 12 b82

Download or read book A method for the numerical solution of the one-dimensional inverse Stefan problem written by 12 b82 and published by . This book was released on 1982 with total page 21 pages. Available in PDF, EPUB and Kindle. Book excerpt:

On the Inverse Multiphase Stefan Problem

Author : Bruno Giuseppe Poggi Cevallos
Publisher :
ISBN 13 :
Total Pages : 100 pages
Book Rating : 4.:/5 (928 download)

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Book Synopsis On the Inverse Multiphase Stefan Problem by : Bruno Giuseppe Poggi Cevallos

Download or read book On the Inverse Multiphase Stefan Problem written by Bruno Giuseppe Poggi Cevallos and published by . This book was released on 2015 with total page 100 pages. Available in PDF, EPUB and Kindle. Book excerpt: We consider inverse multiphase Stefan problem, where information on the heat flux on the fixed boundary is missing and must be found along with the temperature and free boundaries. Optimal control framework is pursued, where boundary heat flux is the control, and optimality criteria consists of the minimization of the L2-norm declination of the trace of the solution to the Stefan problem from the temperature measurement on the fixed boundary. State vector solves multiphase Stefan problem in a weak formulation, which is equivalent to Neumann problem for the quasilinear parabolic PDE with discontinuous coefficient. Full discretization through finite differences is implemented and discrete optimal control problem is introduced. We prove wellposedness in Sobolev spaces framework and convergence of discrete optimal control problems to the original problem both with respect to cost functional and control. Along the way the convergence of the method of finite differences for the weak solution of the multiphese Stefan problem is proved. The proof is based on the proof of uniform L[infinity] bound, and W21 1-energy estimate for the discrete multi phase Stefan problem.

Inverse Problems in Engineering Mechanics II

Author : G.S. Dulikravich
Publisher : Elsevier
ISBN 13 : 0080535151
Total Pages : 607 pages
Book Rating : 4.0/5 (85 download)

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Book Synopsis Inverse Problems in Engineering Mechanics II by : G.S. Dulikravich

Download or read book Inverse Problems in Engineering Mechanics II written by G.S. Dulikravich and published by Elsevier. This book was released on 2000-12-11 with total page 607 pages. Available in PDF, EPUB and Kindle. Book excerpt: Inverse Problems are found in many areas of engineering mechanics and there are many successful applications e.g. in non-destructive testing and characterization of material properties by ultrasonic or X-ray techniques, thermography, etc. Generally speaking, inverse problems are concerned with the determination of the input and the characteristics of a system, given certain aspects of its output. Mathematically, such problems are ill-posed and have to be overcome through development of new computational schemes, regularization techniques, objective functionals, and experimental procedures. Following the IUTAM Symposium on these topics, held in May 1992 in Tokyo, another in November 1994 in Paris, and also the more recent ISIP'98 in March 1998 in Nagano, it was concluded that it would be fruitful to gather regularly with researchers and engineers for an exchange of the newest research ideas. The most recent Symposium of this series "International Symposium on Inverse Problems in Engineering Mechanics (ISIP2000)" was held in March of 2000 in Nagano, Japan, where recent developments in inverse problems in engineering mechanics and related topics were discussed. The following general areas in inverse problems in engineering mechanics were the subjects of ISIP2000: mathematical and computational aspects of inverse problems, parameter or system identification, shape determination, sensitivity analysis, optimization, material property characterization, ultrasonic non-destructive testing, elastodynamic inverse problems, thermal inverse problems, and other engineering applications. The papers in these proceedings provide a state-of-the-art review of the research on inverse problems in engineering mechanics and it is hoped that some breakthrough in the research can be made and that technology transfer will be stimulated and accelerated due to their publication.

Statistical and Computational Inverse Problems

Author : Jari Kaipio
Publisher : Springer Science & Business Media
ISBN 13 : 0387271325
Total Pages : 346 pages
Book Rating : 4.3/5 (872 download)

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Book Synopsis Statistical and Computational Inverse Problems by : Jari Kaipio

Download or read book Statistical and Computational Inverse Problems written by Jari Kaipio and published by Springer Science & Business Media. This book was released on 2006-03-30 with total page 346 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book covers the statistical mechanics approach to computational solution of inverse problems, an innovative area of current research with very promising numerical results. The techniques are applied to a number of real world applications such as limited angle tomography, image deblurring, electical impedance tomography, and biomagnetic inverse problems. Contains detailed examples throughout and includes a chapter on case studies where such methods have been implemented in biomedical engineering.

Differential Equations

Author : Angelo Favini
Publisher : CRC Press
ISBN 13 : 1420011138
Total Pages : 303 pages
Book Rating : 4.4/5 (2 download)

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Book Synopsis Differential Equations by : Angelo Favini

Download or read book Differential Equations written by Angelo Favini and published by CRC Press. This book was released on 2006-06-09 with total page 303 pages. Available in PDF, EPUB and Kindle. Book excerpt: With contributions from some of the leading authorities in the field, the work in Differential Equations: Inverse and Direct Problems stimulates the preparation of new research results and offers exciting possibilities not only in the future of mathematics but also in physics, engineering, superconductivity in special materials, and other scientifi