Journal ArticleDOI
Time Dependent Free Boundary Problems
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In this article, the existence and continuity of solutions and the shape and smoothness of the free boundary of a dam with time were investigated for the flow of liquid in a dam.Abstract:
Recent results on the existence and continuity of solutions, and on the shape and smoothness of the free boundary are described for the following problems: (a) the flow of liquid in a dam with time...read more
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Journal ArticleDOI
A bibliography on moving-free boundary problems for the heat-diffusion equation. The stefan and related problems
TL;DR: Tarzia et al. as discussed by the authors presented a bibliografía on moving and free boundary problems for the heatdiffusion equation, particularly regarding the Stefan and related problems, which contains 5869 titles referring to 588 scientific journals, 122 books, 88 symposia, 30 collections, 59 thesis and 247 technical reports.
Journal ArticleDOI
Classical solutions of multidimensional Hele-Shaw models
Joachim Escher,Gieri Simonett +1 more
TL;DR: In this paper, the existence and uniqueness of classical solutions for the multidimensional expanding Hele-Shaw problem are proved, and a new solution for this problem is proposed.
Journal ArticleDOI
On the Stefan problem
TL;DR: In this article, a general statement of the Stefan problem and some of its variants is given, and the method of integral functionals with a variable domain of integration is presented. And the many-dimensional non-stationary problem is discussed.
Journal ArticleDOI
Steady periodic flow through a rectangular dam
TL;DR: For unsteady free surface flow in a rectangular dam, a simple integral relation which connects the pressure integral with the movement of the free surface is derived in this paper, which leads to an average discharge formula which is a generalization of the Dupuit-Forchheimer discharge formula.
Journal ArticleDOI
Well-posedness of two-phase Darcy flow in 3D
TL;DR: In this paper, the authors prove the well-posedness of the motion of two fluids flowing according to Darcy's law, separated by a sharp interface in the absence of surface tension.
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