Volterra integral equations and evolution equations with an integral condition

Volterra integral equations and evolution equations with an integral condition We suggest a simple method for reducing problems with an integral condition for evolution equations to a Volterra integral equation of the first kind. For Volterra equations of the convolution type, we indicate necessary and sufficient solvability conditions for the case in which the right-hand side lies in some classes of functions of finite smoothness. We use these conditions to construct examples of nonexistence of a local solution for the heat equation with an integral condition. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Differential Equations Springer Journals

Volterra integral equations and evolution equations with an integral condition

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Publisher
Pleiades Publishing
Copyright
Copyright © 2017 by Pleiades Publishing, Ltd.
Subject
Mathematics; Ordinary Differential Equations; Partial Differential Equations; Difference and Functional Equations
ISSN
0012-2661
eISSN
1608-3083
D.O.I.
10.1134/S0012266117070011
Publisher site
See Article on Publisher Site

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