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Appearance of mushy regions in a symmetrical Stefan problem with vanishing heat capacity†

Published online by Cambridge University Press:  16 July 2009

Pedro R. Marangunic  and
Mirta B. Stampella
Pedro R. Marangunic
Affiliation:
Instituto de Matemática ‘B. Levi’, Universidad Nacional de Rosario, Av. Pellegrini 250, 2000 Rosario, Argentina
Mirta B. Stampella
Affiliation:
Instituto de Matemática ‘B. Levi’, Universidad Nacional de Rosario, Av. Pellegrini 250, 2000 Rosario, Argentina
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Abstract

We prove that in the Stefan problem with planar, cylindrical or spherical symmetry, with vanishing heat capacity and constant boundary temperature, no mushy region can appear, even in the presence of constant volumetric heat sources, if the initial data are consistent with the presence of just two pure phases. If the boundary temperature is not constant, a mushy region may or may not appear; we find some general conditions ensuring one case or the other and we give a specific example illustrating the appearance of a mushy region.

Type
Research Article
Information
European Journal of Applied Mathematics , Volume 1 , Issue 2 , June 1990 , pp. 177 - 187
Copyright
Copyright © Cambridge University Press 1990

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References

Fasano, A. 1987 Las zonas pastosas en el problema de Stefan. CUADERNOS Inst. Mat. ‘B. Levi’, n. 13, Univ. Nac. Rosario.Google Scholar
Fasano, A. & Primicerio, M. 1985a Mushy regions with variable temperature in melting processes. Boll. U.M.I. 4B, 601–626.Google Scholar
Fasano, A. & Primicerio, M. 1985b Phase-change with volumetric heat sources: Stefan's scheme vs. enthalpy formulation. Boll. U.M.I. Suppl. Fis. Matem. 4, 131–149.Google Scholar
Fasano, A. & Primicerio, M. 1989 Phase change without sharp interfaces. In: Proc. European Workshop on ‘Mathematical models for phase change problems’ 10 1–3, 1988, Óbidos, , Portugal, ed. Rodrigues, J. F., pp. 107–125. Birkhäuser Verlag, Basel.CrossRefGoogle Scholar
Howison, S. D., Ockendon, J. R. & Lacey, A. A. 1985 Singularity development in moving- boundary problems. Q. J. Mech. AppI. Math. 38, 343–360.CrossRefGoogle Scholar
Meirmanov, A. M. 1981 An example of nonexistence of a classical solution of the Stefan problem. Soviet Math. Dokl. 23, 564–566.Google Scholar
Piccinini, L. C., Stampacchia, G. & Vidossich, G. 1984 Ordinary Differential Equations in Rn. Problems and Methods. Springer-Verlag.Google Scholar
Primicerio, M. 1983 Mushy regions in phase-change problems. In: Proc. Applied Nonlinear Functional Analysis (ed. Hoffmann, K. H. & Gorenflo, R.), pp. 251–269. Verlag Peter Lang, Frankfurt.Google Scholar
Rogers, J. C. W. & Berger, A. E. 1984 Some properties of the nonlinear semigroup for the problem μt–Δf(μ) = 0. Nonlinear Anal. Th. Appl. 8, 909–939.CrossRefGoogle Scholar