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Stability of bounded solutions of linear functional equations


Author: Joel N. Franklin
Journal: Math. Comp. 25 (1971), 413-424
MSC: Primary 47A50; Secondary 35R25
DOI: https://doi.org/10.1090/S0025-5718-1971-0380461-7
MathSciNet review: 0380461
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Abstract: The weak sequential compactness of reflexive Banach spaces is used to explain the fact that certain ill-posed, linear problems become well-posed if the solutions are required to satisfy a prescribed bound. Applications are made to the computability of solutions of ill-posed problems associated with elliptic and parabolic partial differential equations.


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

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Additional Information

DOI: https://doi.org/10.1090/S0025-5718-1971-0380461-7
Keywords: Well-posed, ill-posed, continuous dependence on data, stability, backwards heat-equation, final-value problem, elliptic continuation
Article copyright: © Copyright 1971 American Mathematical Society