We consider a second-order equation with a linear “elastic” part and a nonlinear damping term depending on a power of the norm of the velocity. We investigate the asymptotic behavior of solutions, after rescaling them suitably in order to take into account the decay rate and bound their energy away from zero. We find a rather unexpected dichotomy phenomenon. Solutions with finitely many Fourier components are asymptotic to solutions of the linearized equation without damping and exhibit some sort of equipartition of the total energy among the components. Solutions with infinitely many Fourier components tend to zero weakly but not strongly. We show also that the limit of the energy of the solutions depends only on the number of their Fourie...
AbstractWe study the problem of decay rate for the solutions of the initial–boundary value problem t...
We study the so-called damped Navier-Stokes equations in the whole 2D space. The global well-posedne...
In this paper, we obtain optimal decay estimates for the solutions to an evolution equation with cri...
We consider a second-order equation with a linear "elastic" part and a nonlinear damping term depend...
We consider a second order equation with a linear ``elastic'' part and a nonlinear damping term depe...
We consider an abstract second order evolution equation with damping. The ``elastic'' term is repre...
We consider an abstract second order non-autonomous evolution equation in a Hilbert space H : u″ + A...
International audienceIn this paper we consider second order evolution equations with bounded dampin...
We study the best possible energy decay rates for a class of linear secondorder dissipative evolutio...
Under suitable growth and coercivity conditions on the nonlinear damping operator g which ensure non...
This paper develops a unified method to derive decay estimates for general second order integro-diff...
AbstractThis paper develops a unified method to derive decay estimates for general second order inte...
In this thesis we study global smooth solutions of certain Hamiltonian PDEs, in order to capture the...
International audienceWe consider an unpinned chain of harmonic oscillators with periodic boundary c...
Abstract. We study the asymptotic behavior of energy for wave equations with nonlinear damping g(ut)...
AbstractWe study the problem of decay rate for the solutions of the initial–boundary value problem t...
We study the so-called damped Navier-Stokes equations in the whole 2D space. The global well-posedne...
In this paper, we obtain optimal decay estimates for the solutions to an evolution equation with cri...
We consider a second-order equation with a linear "elastic" part and a nonlinear damping term depend...
We consider a second order equation with a linear ``elastic'' part and a nonlinear damping term depe...
We consider an abstract second order evolution equation with damping. The ``elastic'' term is repre...
We consider an abstract second order non-autonomous evolution equation in a Hilbert space H : u″ + A...
International audienceIn this paper we consider second order evolution equations with bounded dampin...
We study the best possible energy decay rates for a class of linear secondorder dissipative evolutio...
Under suitable growth and coercivity conditions on the nonlinear damping operator g which ensure non...
This paper develops a unified method to derive decay estimates for general second order integro-diff...
AbstractThis paper develops a unified method to derive decay estimates for general second order inte...
In this thesis we study global smooth solutions of certain Hamiltonian PDEs, in order to capture the...
International audienceWe consider an unpinned chain of harmonic oscillators with periodic boundary c...
Abstract. We study the asymptotic behavior of energy for wave equations with nonlinear damping g(ut)...
AbstractWe study the problem of decay rate for the solutions of the initial–boundary value problem t...
We study the so-called damped Navier-Stokes equations in the whole 2D space. The global well-posedne...
In this paper, we obtain optimal decay estimates for the solutions to an evolution equation with cri...