Stability of bounded solutions of linear functional equations-Reference-Cited by-同舟云学术

Stability of bounded solutions of linear functional equations

Published:1971 Issue:115 Volume:25 Page:413-424
ISSN:0025-5718
Container-title:Mathematics of Computation
language:en
Short-container-title:Math. Comp.

Author:

Franklin Joel N.

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.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,Computational Mathematics,Algebra and Number Theory

Link

http://www.ams.org/mcom/1971-25-115/S0025-5718-1971-0380461-7/S0025-5718-1971-0380461-7.pdf

Reference11 articles.

1. J. Hadamard, Lectures on Cauchy’s Problem in Linear Partial Differential Equations, Yale Univ. Press, New Haven, Conn., 1923.

2. Numerical solution of the equation of heat conduction for preceding times;John, Fritz;Ann. Mat. Pura Appl. (4),1955

3. Numerical solution of problems which are not well posed in the sense of Hadamard;John, Fritz,1959

4. Continuous dependence on data for solutions of partial differential equations with a presribed bound;John, Fritz;Comm. Pure Appl. Math.,1960

5. On some non well posed problems for partial differential equations;Payne, L. E.,1966

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