A free boundary value problem related to the combustion of a solid: flux boundary conditions

Authors:
John R. Cannon and Alec L. Matheson

Journal:
Quart. Appl. Math. **55** (1997), 687-705

MSC:
Primary 35R35; Secondary 35K57, 80A25

DOI:
https://doi.org/10.1090/qam/1486543

MathSciNet review:
MR1486543

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Abstract | References | Similar Articles | Additional Information

Abstract: We demonstrate the existence, uniqueness, and continuous dependence upon the data for the solution of the free boundary value problem:

**[C]**John. R. Cannon,*The one-dimensional heat equation*, Encyclopedia of Mathematics, Addison-Wesley, Reading, MA, 1984 MR**747979****[CCF]**John R. Cannon, James C. Cavendish, and Antonio Fasano,*A free boundary-value problem related to the combustion of a solid*, SIAM J. Appl. Math.**45**798-809 (1985) MR**804007****[CL]**John R. Cannon and Yanping Lin,*A free boundary-value problem related to the combustion of a solid: first initial-boundary value case*, Proc. of the Intl. Conf. on Theory and Appl. of Diff. Eq. (Reza Aftabizadeh, ed.), Ohio University Press, Athens, Ohio, 1989, pp. 109-121 MR**1026123****[F]**A. Fasano,*A free boundary value problem in combustion*, Nonlinear parabolic equations: qualitative properties of solutions, Pitman Research Notes, Math Series, Longman Sci. Tech., Harlow, 1987 MR**901097****[FR]**A. Friedman,*Free boundary problem for parabolic equations*: I.*Melting of solids*, J. Math. Mech.**8**499-517 (1959) MR**0144078****[LC]**Xhi Yuan Liang and Hong Cheng,*A class of free boundary problems with two boundaries arising in combustion of solids*, J. Harbin Inst. Tech.**24**1-6 (1992) MR**1178246**

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Additional Information

DOI:
https://doi.org/10.1090/qam/1486543

Article copyright:
© Copyright 1997
American Mathematical Society