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

TL;DR

This paper investigates the global existence of solutions for a nonlinear second-order dissipative dynamical system with a time-varying nonnegative friction coefficient and an internal constraint, contributing to the understanding of such models.

Contribution

It establishes conditions for the global existence of solutions in a heavy ball model with a varying friction coefficient and internal constraints.

Findings

Proves global existence under specific conditions on mbda(t)

Analyzes the impact of non-negative, time-dependent friction on system behavior

Provides mathematical framework for dissipative systems with constraints

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 $\Phi \in \mathcal{C}^2$.