Displaying similar documents to “Compact attractor for weakly damped driven Korteweg-de Vries equations on the real line”

Stability of vibrations for some Kirchhoff equation with dissipation

Prasanta Kumar Nandi, Ganesh Chandra Gorain, Samarjit Kar (2014)

Applications of Mathematics

Similarity:

In this paper we consider the boundary value problem of some nonlinear Kirchhoff-type equation with dissipation. We also estimate the total energy of the system over any time interval [ 0 , T ] with a tolerance level γ . The amplitude of such vibrations is bounded subject to some restrictions on the uncertain disturbing force f . After constructing suitable Lyapunov functional, uniform decay of solutions is established by means of an exponential energy decay estimate when the uncertain disturbances...

Transition from decay to blow-up in a parabolic system

Pavol Quittner (1998)

Archivum Mathematicum

Similarity:

We show a locally uniform bound for global nonnegative solutions of the system u t = Δ u + u v - b u , v t = Δ v + a u in ( 0 , + ∞ ) × Ω , u = v = 0 on ( 0 , + ∞ ) × ∂ Ω , where a > 0 , b ≥ 0 and Ω is a bounded domain in ℝ n , n ≤ 2 . In particular, the trajectories starting on the boundary of the domain of attraction of the zero solution are global and bounded.

Stabilization of Berger–Timoshenko’s equation as limit of the uniform stabilization of the von Kármán system of beams and plates

G. Perla Menzala, Ademir F. Pazoto, Enrique Zuazua (2002)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

Similarity:

We consider a dynamical one-dimensional nonlinear von Kármán model for beams depending on a parameter ε > 0 and study its asymptotic behavior for t large, as ε → 0 . Introducing appropriate damping mechanisms we show that the energy of solutions of the corresponding damped models decay exponentially uniformly with respect to the parameter ε . In order for this to be true the damping mechanism has to have the appropriate scale with respect to ε . In the limit as ε → 0 we obtain damped Berger–Timoshenko...