# American Institute of Mathematical Sciences

2013, 2013(special): 477-487. doi: 10.3934/proc.2013.2013.477

## Existence of sliding motions for nonlinear evolution equations in Banach spaces

 1 Free University of Bolzano/Bozen, Piazza Università 1, 39100 Bolzano, Italy

Received  September 2012 Revised  September 2013 Published  November 2013

In this paper the issue of existence of sliding motions for a class of control systems of parabolic type is considered. The operator satisfies standard hemicontinuity, monotonicity and coercivity assumptions; the control law is finite-dimensional and enters linearly in the equation. By using a Faedo-Galerkin approach, a family of finite-dimensional ODEs is constructed and an approximating sequence of sliding motions is obtained using classical variable structure control techniques. Previous results on the convergence of the approximations are extended, by taking into consideration more general growth assumptions on the feedbacks. A detailed description of the approach for semilinear partial differential equations with Neumann boundary control is discussed.
Citation: Laura Levaggi. Existence of sliding motions for nonlinear evolution equations in Banach spaces. Conference Publications, 2013, 2013 (special) : 477-487. doi: 10.3934/proc.2013.2013.477
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