Electron. J. Differential Equations, Vol. 2018 (2018), No. 10, pp. 1-12.

One-phase Stefan problem with a latent heat depending on the position of the free boundary and its rate of change

Julieta Bollati, Domingo A. Tarzia

Abstract:
From the one-dimensional consolidation of fine-grained soils with threshold gradient, it can be derived a special type of Stefan problems where the seepage front, because of the presence of this threshold gradient, exhibits the features of a moving boundary. In this type of problems, in contrast with the classical Stefan problem, the latent heat is considered to depend inversely to the rate of change of the seepage front. In this paper, we study a one-phase Stefan problem with a latent heat that depends on the rate of change of the free boundary and on its position. The aim of this analysis is to extend prior results, finding an analytical solution that recovers, by specifying some parameters, the solutions that have already been examined in the literature regarding Stefan problems with variable latent heat. Computational examples are presented to examine the effect of this parameters on the free boundary.

Submitted May 26, 2017. Published January 8, 2018
Math Subject Classifications: 35R35, 80A22, 35C05, 35C06.
Key Words: Stefan problem; threshold gradient; variable latent heat; one-dimensional consolidation; explicit solution; similarity solution.

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Julieta Bollati
Depto. Matemática - CONICET, FCE
Univ. Austral, Paraguay 1950
S2000FZF Rosario, Argentina
email: JBollati@austral.edu.ar
Domingo A. Tarzia
Depto. Matemática - CONICET, FCE
Univ. Austral, Paraguay 1950
S2000FZF Rosario, Argentina
email: DTarzia@austral.edu.ar

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