Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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



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

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