Fan's minimax inequality is extended to the context of metric spaces with global nonpositive curvature. As a consequence, a much more general result on the existence of a Nash equilibrium is obtained.
We consider a finite difference semi-discrete scheme for the approximation of the boundary controls of a 1-D equation modelling the transversal vibrations of a hinged beam. It is known that, due to the high frequency numerical spurious oscillations, the uniform (with respect to the mesh-size) controllability property of the semi-discrete model fails in the natural setting. Consequently, the convergence of the approximate controls corresponding to initial data in the finite energy space cannot be guaranteed. We prove that, by adding a vanishing numerical viscosity, the uniform controllability property and the convergence of the scheme is ensured.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.