Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



The Stefan problem with arbitrary initial and boundary conditions

Author: L. N. Tao
Journal: Quart. Appl. Math. 36 (1978), 223-233
MSC: Primary 80A10; Secondary 35K20
DOI: https://doi.org/10.1090/qam/508769
MathSciNet review: 508769
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Abstract: The paper is concerned with the free boundary problem of a semi-infinite body with an arbitrarily prescribed initial condition and an arbitrarily prescribed boundary condition at its face. An analytically exact solution of the problem is established, which is expressed in terms of some functions and polynomials of the similarity variable $ x/{t^{1/2}}$ and time $ t$. Convergence of the series solution is considered and proved. Hence the solution also serves as an existence proof. Some special initial and boundary conditions are discussed, which include the Neumann problem and the one-phase problem as special cases.

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DOI: https://doi.org/10.1090/qam/508769
Article copyright: © Copyright 1978 American Mathematical Society

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