Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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Temporary range of validity for some mathematical models which involve the heat-diffusion equation


Author: Lucio R. Berrone
Journal: Quart. Appl. Math. 54 (1996), 1-19
MSC: Primary 35K05; Secondary 80A20
DOI: https://doi.org/10.1090/qam/1373835
MathSciNet review: MR1373835
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Abstract | References | Similar Articles | Additional Information

Abstract: We study different initial and boundary value problems for the one-dimensional heat-diffusion equation, with the purpose of establishing conditions on initial and boundary data that ensure the solution is, during a certain interval of time, bounded by two predetermined constants. When the constants represent phase-change temperatures of a material medium, the desired conditions can be physically interpreted by saying that the medium does not undergo a phase-change during a certain lapse of time; i.e., the heat-conduction model will preserve its validity in the meantime. The tools employed to tackle this kind of problem consist in reducing the initial and boundary value problems to a Volterra integral equation. For these equations there exist simple methods to estimate their solutions. We improve some results that appeared in [8].


References [Enhancements On Off] (What's this?)

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  • [7] D. A. Tarzia, An inequality for the coefficient $ \sigma $ of the free boundary $ s\left( t \right) = 2\sigma \sqrt t $ of the Neumann solution for the two-phase Stefan problem, Quart. Appl. Math. 39, 491-497 (1981)
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Additional Information

DOI: https://doi.org/10.1090/qam/1373835
Article copyright: © Copyright 1996 American Mathematical Society


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