International Journal of Mathematics and Mathematical Sciences
Volume 7 (1984), Issue 2, Pages 409-411
doi:10.1155/S0161171284000430
On the existence of equations of evolution
J. Lubliner
Department of Civil Engineering, University of California, Berkeley 94720, California, USA
Abstract
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.