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International Journal of Mathematics and Mathematical Sciences
Volume 7 (1984), Issue 2, Pages 409-411

On the existence of equations of evolution

Department of Civil Engineering, University of California, Berkeley 94720, California, USA

Received 27 March 1983

Copyright © 1984 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


A time-independent, non-autonomous non-linear system governed by a principle of determinism (the state at a given time is determined by the initial state and by the control history during the intervening closed interval) is shown to obey a generalized evolution equation (1.2), where n is such that the state is continuously differentiabie with respect to time whenever the control is of class Cn.