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Stefan problem
About: Stefan problem is a research topic. Over the lifetime, 2267 publications have been published within this topic receiving 63234 citations.
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Book•
31 Dec 1959
TL;DR: In this paper, a classic account describes the known exact solutions of problems of heat flow, with detailed discussion of all the most important boundary value problems, including boundary value maximization.
Abstract: This classic account describes the known exact solutions of problems of heat flow, with detailed discussion of all the most important boundary value problems.
21,807 citations
Book•
01 Jan 1980
TL;DR: In this paper, the SIAM edition Preface Glossary of notations Introduction Part I. Variational Inequalities in Rn Part II. Free Boundary Problems Governed by Elliptic Equations and Systems Part VII. A One Phase Stefan Problem Bibliography Index.
Abstract: Preface to the SIAM edition Preface Glossary of notations Introduction Part I. Variational Inequalities in Rn Part II. Variational Inequalities in Hilbert Space Part III. Variational Inequalities for Monotone Operators Part IV. Problems of Regularity Part V. Free Boundary Problems and the Coincidence Set of the Solution Part VI. Free Boundary Problems Governed by Elliptic Equations and Systems Part VII. Applications of Variational Inequalities Part VIII. A One Phase Stefan Problem Bibliography Index.
4,107 citations
Book•
01 Jan 1984
TL;DR: In this paper, a front-tracking method is used to solve moving boundary problems and an analytical solution of seepage problems is proposed. But this method is not suitable for solving free boundary problems.
Abstract: 1. Moving boundary problems: formulation 2. Free boundary problems: formulation 3. Analytical solutions 4. Front-tracking methods 5. Front-fixing methods 6. Fixed-domain methods 7. Analytical solution of seepage problems 8. Numerical solution of free boundary problems References Author index Subject index
1,880 citations
Book•
01 Jan 1984TL;DR: In this paper, Browder et al. considered the initial-boundary value problem for the semi-infinite strip with temperature and flux-flux-boundaries specification.
Abstract: Editor's statement Foreword Felix E. Browder Preface Preliminaries 1. Introduction 2. The Cauchy problem 3. The initial-value problem 4. The initial-boundary-value problem for the quarter plane with temperature-boundary specification 5. The initial-boundary-value problem for the quarter plane with heat-flux-boundary specification 6. The initial-boundary-value problem for the semi-infinite strip with temperature-boundary specification and heat-flux-boundary specification 7. The reduction of some initial-boundary-value problems for the semi-infinite strip, to integral equations: some exercises 8. Integral equations 9. Solutions of boundary-value problems for all times and periodic solutions 10. Analyticity of solutions 11. Continuous dependence upon the data for some state-estimation problems 12. Some numerical methods for some state-estimation problems 13. Determination of an unknown time-dependent diffusivity a(t) from overspecified data 14. Initial- and/or boundary-value problems for gneral regions with Holder continuous boundaries 15. Some properties of solutions in general domains 16. The solution in a general region with temperature-boundary specification: the method of perron-poincare 17. The one-phase stefan problem with temperature-boundary specification 18. The one-phase stefan problem with flux-boundary specification: some exercises 19. The inhomogeneous heat equation ut=uxx+f(x,t) 20. An application of the inhomogeneous heat equation: the equation ut=uxx+f(x,t,u,ux) Symbol index Subject index.
781 citations