UID:
almahu_9947360003102882
Format:
Online-Ressource (ix, 244 p)
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ill
Edition:
Online-Ausg. Palo Alto, Calif ebrary 2011 Electronic reproduction; Available via World Wide Web
ISBN:
3110114798 (alk. paper)
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9783110114799 (alk. paper)
Series Statement:
De Gruyter expositions in mathematics 3
Uniform Title:
Zadacha Stefana. ‹engl.›
Content:
The Stefan Problem (Kirchen Der Welt)
Note:
Includes bibliographical references (p. [231]-244) and index
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Translation of: Zadacha Stefana
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1. The one-phase Stefan problem. Main result2. The simplest problem setting; 3. Construction of approximate solutions to the one-phase Stefan problem over a small time interval; 4. A lower bound on the existence interval of the solution. Passage to the limit; 5. The two-phase Stefan problem; Chapter III. Existence of the classical solution to the multidimensional Stefan problem on an arbitrary time interval; 1. The one-phase Stefan problem; 2. The two-phase Stefan problem. Stability of the stationary solution; 2.1. Problem statement. Main result.
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2. Structure of the mushy phase for temperature on the boundary of Ω∞ with constant sign.
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2.2. Formulation of the equivalent boundary value problem2.3. Construction of approximate solutions; 2.4. A lower bound for the constant δ3; 2.5. Proof of the main result; Chapter IV. Lagrange variables in the multidimensional one-phase Stefan problem; 1. Formulation of the problem in Lagrange variables; 2. Linearization; 3. Correctness of the linear model; Chapter V. Classical solution of the one-dimensional Stefan problem for the homogeneous heat equation; 1. The one-phase Stefan problem. Existence of the solution; 2. Asymptotic behaviour of the solution of the one-phase Stefan problem.
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3. The two-phase Stefan problem4. Special cases: one-phase initial state, violation of compatibility conditions, unbounded domains; 5. The two-phase multi-front Stefan problem; 6. Filtration of a viscid compressible liquid in a vertical porous layer; 6.1. Problem statement. The main result; 6.2. An equivalent boundary value problem in a fixed domain; 6.3. A comparison lemma; 6.4. The case ∫1∞1/f(p)dp = ∞; 6.5. The case f(p) = exp(p - 1); 6.6. The case f(p) = pγ, γ ≥ 1; 6.7. Asymptotic behaviour of the solution, as t→∞.
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Chapter VI. Structure of the generalized solution to the one-phase Stefan problem. Existence of a mushy region1. The inhomogeneous heat equation. Formation of the mushy region; 2. The homogeneous heat equation. Dynamic interactions between the mushy phase and the solid/liquid phases; 3. The homogeneous heat equation. Coexistence of different phases; 4. The case of an arbitrary initial distribution of specific internal energy; Chapter VII. Time-periodic solutions of the one-dimensional Stefan problem; 1. Construction of the generalized solution.
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Preface to the English edition; Preface; Introduction; Chapter I. Preliminaries; 1. Problem statement; 2. Assumed notation. Auxiliary notation; 2.1. Notation; 2.2. Basic function spaces; 2.3. Auxiliary inequalities and embedding theorems; 2.4. Auxiliary facts from analysis; 2.5. Properties of solutions of differential equations; 2.6. The Cauchy problem for the heat equation over smooth unbounded manifolds in the classes Hl+2,(l+2)/2(ST); 3. Existence and uniqueness of the generalized solution to the Stefan problem; Chapter II. Classical solution of the multidimensional Stefan problem.
Additional Edition:
ISBN 9783110846720
Language:
English
DOI:
10.1515/9783110846720
URL:
http://www.degruyter.com/doi/book/10.1515/9783110846720
