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A free boundary problem arising in the modelling of internal oxidation of binary alloys

Published online by Cambridge University Press:  26 September 2008

Bei Hu  and
Jianhua Zhang
Bei Hu
Affiliation:
Department of Mathematics, University of Notre Dame, Notre Dame, IN 46556, USA
Jianhua Zhang
Affiliation:
School of Mathematics, University of Minnesota, Minneapolis, MN 55455, USA
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Abstract

A one-dimensional free boundary problem arising in the modelling of internal oxidation of binary alloys is studied in this paper. The free boundary of this problem is determined by the equation u = 0, where u is the solution of a parabolic partial differential equation with discontinuous coefficients across the free boundary. Local existence, uniqueness and the regularity of the free boundary are established. Global existence is also studied.

Type
Research Article
Information
European Journal of Applied Mathematics , Volume 6 , Issue 3 , June 1995 , pp. 225 - 245
Copyright
Copyright © Cambridge University Press 1995

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References

[1]Friedman, A. 1990 Mathematics in Industrial Problems, Part 3. Springer-Verlag.CrossRefGoogle Scholar
[2]Hagan, P. S., Polizzotti, R. S. & Luckman, G. 1985 Internal oxidation of binary alloys. SIAM J. Appl. Math. 45 (6), 956–971.CrossRefGoogle Scholar
[3]Evans, L. C. 1977 A free boundary problem: the flow of two immiscible fluids in a one dimensional porous Medium, I. Indiana Univ. Math. J. 26, 915–932.CrossRefGoogle Scholar
[4]Evans, L. C. 1977 A free boundary problem: the flow of two immiscible fluids in a one dimensional porous medium, II. Indiana Univ. Math. J. 27, 93–111.CrossRefGoogle Scholar
[5]Fasano, A. & Primicerio, M. 1979 Free boundary problems for nonlinear parabolic equations with nonlinear free boundary conditions. J. Math. Anal. Appl. 72, 247–273.CrossRefGoogle Scholar
[6]Krylov, N. V. 1987 Nonlinear Elliptic and Parabolic Equations of Second Order. Reidel.CrossRefGoogle Scholar
[7]Ladyzhenskaja, O. A., Solonnikov, V. A. & Uraltseva, N. N. 1968 Linear and quasilinear equations of parabolic type. Am. Math. Soc, Providence, RI.Google Scholar
[8]Friedman, A. 1982 Variational Principles and Free Boundary Problems. Wiley.Google Scholar
[9]Solonnikov, V. A. 1967 Boundary value problems of mathematical physics. III Ladyzhenskaja, O. A. (ed.). Am. Math. Soc., Providence, RI.Google Scholar
[10]Friedman, A. 1964 Partial Differential Equations of Parabolic Type. Prentice-Hall.Google Scholar
[11]Tso, K. S. 1985 On an Aleksandrov-Bakelman type maximum principle for second order parabolic equations. Comm. PDE 10, 543–553.Google Scholar
[12]Van Duyn, C. J. & Peletier, L. A. 1982 Nonstationary filtration in partially saturated porous media. Arch. Rat. Mech. Anal. 78, 173–198.CrossRefGoogle Scholar
[13]Fasano, A. & Primicerio, M. 1979 Liquid flow in partially saturated porous media. J. Inst. Maths Applic. 23, 503–517.CrossRefGoogle Scholar