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The Pettis integration of a perturbed wave equation

Published online by Cambridge University Press:  24 October 2008

James P. Fink
James P. Fink
Affiliation:
University of Pittsburgh, Pa 15260, U.S.A.
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Abstract

In this paper, we investigate the integrability of the vector field of the initial-value problem associated with certain nonlinear wave equations. This vector field involves translations and as such is not a strongly continuous or even strongly measurable L∞-valued function. It is shown that such a vector field, although not generally Pettis integrable, does turn out to be so in an important situation. We then indicate how this result can be used to obtain pseudo-solutions of the initial-value problem.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 86 , Issue 1 , July 1979 , pp. 145 - 159
Copyright
Copyright © Cambridge Philosophical Society 1979

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References

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