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 | References | Similar Articles | Additional Information

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.

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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