L2 asymptotic profiles of solutions to linear damped wave equations

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 Solutions of Semilinear Stochastic Wave Equations

Large-time asymptotic properties of solutions to a class of semilinear stochastic wave equations with damping in a bounded domain are considered. First an energy inequality and the exponential bound for a linear stochastic equation are established. Under appropriate conditions, the existence theorem for a unique global solution is given. Next the questions of bounded solutions and the exponenti...

Asymptotic solutions of pseudodifferential wave equations

The aim of this paper is to give an account of some applications of pseudodifferential calculus for solving linear wave equations in the limit of high frequency/short wavelength waves. More specifically, on using as a benchmark the case of electromagnetic waves propagating in a cold isotropic slowly spaceand time-varying plasma, it is shown that, in general, linear plasma waves are governed by ...

Asymptotic Expansion for Damped Wave Equations with Periodic Coefficients

Asymptotic Behavior of Solutions to Half-Linear q-Difference Equations

and Applied Analysis 3 Next we present auxiliary statements which play important roles in proving the main results. Define F : 0,∞ → R by F x Φ x/q−1/q −Φ 1−1/x and h : Φ −∞ q ,∞ → R by h x x 1 − q1−α [ 1 − ( 1 ( q − 1 ) Φ−1 x )1−α] . 2.1 For y : q0 → R \ {0} define the operator L by L [ y ] t Φ ( y ( q2t ) qy ( qt ) − 1 q ) −Φ ( 1 − y t