Asymptotic profiles for damped plate equations with rotational inertia terms

Attractors for Stochastic Strongly Damped Plate Equations with Additive Noise

We study the asymptotic behavior of stochastic plate equations with homogeneous Neumann boundary conditions. We show the existence of an attractor for the random dynamical system associated with the equation.

Asymptotic Expansion for Damped Wave Equations with Periodic Coefficients

Dispersion and Asymptotic Profiles for Kirchhoff Equations

The aim of this article is to describe asymptotic profiles for the Kirchhoff equation, and to establish time decay properties and dispersive estimates for Kirchhoff equations. For this purpose, the method of asymptotic integration is developed for the corresponding linear equations and representation formulae for their solutions are obtained. These formulae are analysed further to obtain the ti...

Precise Asymptotic Behavior of Solutions to Damped Simple Pendulum Equations

We consider the simple pendulum equation −u′′(t) + f(u′(t)) = λ sinu(t), t ∈ I := (−1, 1), u(t) > 0, t ∈ I, u(±1) = 0, where 0 < ≤ 1, λ > 0, and the friction term is either f(y) = ±|y| or f(y) = −y. Note that when f(y) = −y and = 1, we have well known original damped simple pendulum equation. To understand the dependance of solutions, to the damped simple pendulum equation with λ 1, upon the te...

Asymptotic behaviour of strongly damped nonlinear hyperbolic equations

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