arXiv subjects

M. Daoulatli

Publications and source records attributed to M. Daoulatli.

3 recordsLinked to original sources

arXiv2017

Behaviors of the energy of solutions of two coupled wave equations with nonlinear damping on a compact manifold with boundary

In this paper we study the behaviors of the the energy of solutions of coupled wave equations on a compact manifold with boundary in the case of indirect nonlinear damping . Only one of the two equations is directly damped by a localized nonlinear damping term. Under geometric conditions on both the coupling and the damping regions we prove that the rate of decay of the energy of smooth solutions of the system is determined from a first order differential equation .

math.AP↗

arXiv2012

Local energy decay for the wave equation with nonlinear time dependent damping

This paper addresses a wave equation on a exterior domain in R^{d}(d odd) with nonlinear time dependent dissipation. Under a microlocal geometric condition we prove that the decay rates of the local energy functional are obtained by solving a nonlinear non-autonomous differential equation.

math.OC↗

arXiv2012

Energy decay rates for solutions of the wave equation with linear damping in exterior domain

In this paper we study the behavior of the energy of solutions of the wave equation with localized damping in exterior domain. We assume that the damper is positive at infinity. Under the Geometric Control Condition of Bardos et al (1992), we prove that: 1) The total energy decay like O(1/t) and L^2-norm is bounded for the solutions with initial data in (H_{0}^{1},L^{2}). 2) The total energy and the square of the L^2-norm, repectively, decay like O(1/t^{2}) and O(1/t) for a kind of the weighted initial data.

math.OC↗