Global existence of a heavy ball model with a varying nonnegative friction

Abstract

In this paper, we study a dissipative dynamical system non linear of second order $\ddot{x}(t)+\lambda (t)\dot{x}(t)+\nabla \Phi (x(t))=0,$ with the non-negative friction coefficient $\lambda \in \mathcal{C}([0,+\infty [)$ and the internal constraint $\Phi \in {\mathcal{C}}^2$.

arXiv comment10 pages, in French