Abstract
Optimal decay estimates for solutions to damped second order ODE's
Highlights
In this paper we study long-time behavior for solutions of damped second order ordinary differential equations u + g(u ) + ∇E(u) = 0, (SOP)
Where E ∈ C2(Ω), Ω being an open connected subset of Rn and g : Rn → Rn is a C1-function satisfying g(v), v ≥ 0 on Rn. This last condition means that the term g(u ) in (SOP) has a damping effect
If u : [0, +∞) → Ω is a global solution and φ belongs to the ω-limit set of u, E (u(t), u (t)) → E (φ, 0) = E(φ) as t → +∞
Summary
We will assume that E satisfies an inverse to (KLI) and some estimates on the second gradient and that g has certain behavior near zero. It is easy to see that admissible functions are C-sublinear and have property (K) (for proof see Appendix of [4]). For nondecreasing functions property (K) is equivalent to C-sublinearity.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
