An Inverse Stefan Problem
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Inverse Stefan Problems
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Author : N.L. Gol'dman
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Inverse Stefan Problems written by N.L. Gol'dman and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
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.
An Inverse Stefan Problem
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Author : Alun H. Williams
language : en
Publisher:
Release Date : 1989
An Inverse Stefan Problem written by Alun H. Williams and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989 with Boundary value problems categories.
The Inverse Stefan Problem For The Heat Equation In Two Space Variables
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Author : David L. Colton
language : en
Publisher:
Release Date : 1974
The Inverse Stefan Problem For The Heat Equation In Two Space Variables written by David L. Colton and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1974 with categories.
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.
The Classical Stefan Problem
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Author : S.C. Gupta
language : en
Publisher: Elsevier
Release Date : 2017-07-27
The Classical Stefan Problem written by S.C. Gupta and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-07-27 with Science categories.
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 Numerical Solution Of The Inverse Stefan Problem In Two Space Variables
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Author : David Colton
language : de
Publisher:
Release Date : 1983
The Numerical Solution Of The Inverse Stefan Problem In Two Space Variables written by David Colton and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1983 with categories.
The Stefan Problem
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Author : L. I. Rubinšteĭn
language : en
Publisher: American Mathematical Soc.
Release Date : 2000-01-25
The Stefan Problem written by L. I. Rubinšteĭn and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-01-25 with categories.
Translations of Mathematical Monographs
Solution Of Inverse Stefan Problem Using A New Enthalpy Method
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Author : Mulugeta K. Berhe
language : en
Publisher:
Release Date : 1995
Solution Of Inverse Stefan Problem Using A New Enthalpy Method written by Mulugeta K. Berhe and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995 with categories.
A Method For The Numerical Solution Of The One Dimensional Inverse Stefan Problem
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Author : Rembert Reemtsen
language : de
Publisher:
Release Date : 1982
A Method For The Numerical Solution Of The One Dimensional Inverse Stefan Problem written by Rembert Reemtsen and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1982 with categories.
A Method For The Numerical Solution Of The One Dimensional Inverse Stefan Problem
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Author : 12 b82
language : de
Publisher:
Release Date : 1982
A Method For The Numerical Solution Of The One Dimensional Inverse Stefan Problem written by 12 b82 and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1982 with categories.
On The Inverse Multiphase Stefan Problem
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Author : Bruno Giuseppe Poggi Cevallos
language : en
Publisher:
Release Date : 2015
On The Inverse Multiphase Stefan Problem written by Bruno Giuseppe Poggi Cevallos and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015 with categories.
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.