A second-order differential system with hessian-driven damping; application to non-elastic shock laws

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Convergence of iterates for first-order optimization algorithms with inertia and Hessian driven damping (2021, background): “The Hessian driven damping was first introduced in [24,25] when combined with a viscous damping term whose coefficient is fixed.”
Fast optimization via inertial dynamics with closed-loop damping (2020, methodology): “This property has been exploited by Attouch–Maingé–Redont [29] for modeling non-elastic shocks in unilateral mechanics.”
Understanding the acceleration phenomenon via high-resolution differential equations (2018, methodology): “Notably, there is a venerable line of work that studies inertial dynamics with a Hessian-driven term [1,7,9,10].”