The monotone method for controllability of the nonlinear evolution systems

2011 ◽  
Vol 27 (4) ◽  
pp. 721-726 ◽  
Author(s):  
Yue Lu ◽  
Yong Li ◽  
Ming-ji Liu
Keyword(s):  
Nonlinear Evolution ◽  
Monotone Method ◽  
Evolution Systems

Approximation of Nonlinear Evolution Systems (Joseph W. Jerome)

SIAM Review ◽  
1987 ◽  
Vol 29 (3) ◽  
pp. 493-495
Author(s):  
R. E. Showalter
Keyword(s):  
Nonlinear Evolution ◽  
Evolution Systems

scholarly journals Evolutionary quasi-variational and variational inequalities with constraints on the derivatives

2018 ◽  
Vol 9 (1) ◽  
pp. 250-277 ◽  
Author(s):  
Fernando Miranda ◽  
José Francisco Rodrigues ◽  
Lisa Santos
Keyword(s):  
Variational Inequalities ◽  
General Framework ◽  
Convex Sets ◽  
Nonlinear Evolution ◽  
Strong Solutions ◽  
Linear Operators ◽  
Variational Solutions ◽  
Derivatives Of ◽  
Monotone Type ◽  
Evolution Systems

Abstract This paper considers a general framework for the study of the existence of quasi-variational and variational solutions to a class of nonlinear evolution systems in convex sets of Banach spaces describing constraints on a linear combination of partial derivatives of the solutions. The quasi-linear operators are of monotone type, but are not required to be coercive for the existence of weak solutions, which is obtained by a double penalization/regularization for the approximation of the solutions. In the case of time-dependent convex sets that are independent of the solution, we show also the uniqueness and the continuous dependence of the strong solutions of the variational inequalities, extending previous results to a more general framework.

Sign in / Sign up

Export Citation Format

Share Document