On the Comparison of Solutions of Related Properly and Improperly Posed Cauchy Problems for First Order Operator Equations

Solutions of Cauchy problems for certain classes of first order operator equations are compared with solutions of associated perturbed equations. We do not require either the original problem or the perturbed problem to be well posed in the sense of Hadamard. The logarithmic convexity method is used...

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Bibliographic Details
Published in:SIAM journal on mathematical analysis 1982-07, Vol.13 (4), p.594-606
Main Author: Ames, Karen A.
Format: Article
Language:English
Subjects:
Cauchy problems
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Summary:Solutions of Cauchy problems for certain classes of first order operator equations are compared with solutions of associated perturbed equations. We do not require either the original problem or the perturbed problem to be well posed in the sense of Hadamard. The logarithmic convexity method is used to derive Holder stability inequalities relating solutions of the perturbed and unperturbed problems in a suitably chosen measure. Several special cases are treated in order to demonstrate how the Lagrange identity method can be employed in the comparison of solutions as well as to indicate how certain data assumptions and requirements on the solutions can be relaxed.
ISSN:0036-1410
1095-7154
DOI:10.1137/0513038