Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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



Continuous dependence results for a problem in penetrative convection

Authors: Karen A. Ames and Lawrence E. Payne
Journal: Quart. Appl. Math. 55 (1997), 769-790
MSC: Primary 35Q35; Secondary 35B30, 76D05, 76R05
DOI: https://doi.org/10.1090/qam/1486548
MathSciNet review: MR1486548
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Abstract: Continuous dependence inequalities are derived for a system of equations that models penetrative convection in a thermally conducting viscous fluid with a linear buoyancy law. Both the forward-in-time problem and the improperly posed backward-in-time problem are analyzed. These results indicate that solutions depend continuously on a parameter in the boundary data.

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DOI: https://doi.org/10.1090/qam/1486548
Article copyright: © Copyright 1997 American Mathematical Society

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