Nonautonomous Projected Dynamical Systems

2009 ◽  
Author(s):  
Monica Gabriela Cojocaru ◽  
Theodore E. Simos ◽  
George Psihoyios ◽  
Ch. Tsitouras
2000 ◽  
Vol 27 (2) ◽  
pp. 83-91 ◽  
Author(s):  
W.P.M.H. Heemels ◽  
J.M. Schumacher ◽  
S. Weiland

2004 ◽  
Vol 2 (1) ◽  
pp. 71-95 ◽  
Author(s):  
George Isac ◽  
Monica G. Cojocaru

In the first part of this paper we present a representation theorem for the directional derivative of the metric projection operator in an arbitrary Hilbert space. As a consequence of the representation theorem, we present in the second part the development of the theory of projected dynamical systems in infinite dimensional Hilbert space. We show that this development is possible if we use the viable solutions of differential inclusions. We use also pseudomonotone operators.


2007 ◽  
Vol 69 (5) ◽  
pp. 1453-1476 ◽  
Author(s):  
Monica-Gabriela Cojocaru ◽  
Chris T. Bauch ◽  
Matthew D. Johnston

2012 ◽  
Vol 2012 ◽  
pp. 1-23 ◽  
Author(s):  
Monica Gabriela Cojocaru ◽  
Stephane Pia

This paper presents a generalization of the concept and uses of projected dynamical systems to the case of nonpivot Hilbert spaces. These are Hilbert spaces in which the topological dual space is not identified with the base space. The generalization consists of showing the existence of such systems and their relation to variational problems, such as variational inequalities. In the case of usual Hilbert spaces these systems have been extensively studied, and, as in previous works, this new generalization has been motivated by applications, as shown below.


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