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].

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DOI:
https://doi.org/10.1090/qam/1373835

Article copyright:
© Copyright 1996
American Mathematical Society