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SMOOTH SOLUTIONS OF VOLTERRA EQUATIONS VIA SEMIGROUPS

Published online by Cambridge University Press:  01 October 2008

TOMÁŠ BÁRTA*
Affiliation:
Faculty of Mathematics and Physics, Department of Mathematical Analysis, Charles University, Prague, Sokolovska 83,180 00 Prague 8, Czech Republic (email: [email protected])
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Abstract

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In this paper we introduce a class of left shift semigroups that are differentiable. With the help of perturbation theory for differentiable semigroups we show that solutions of an integrodifferential equation can be infinitely differentiable if the convolution kernel is sufficiently smooth and regular.

Type
Research Article
Copyright
Copyright © 2008 Australian Mathematical Society

References

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