Marcelo M. Cavalcanti

Existence and uniform decay rates of solutions to a degenerate system with memory conditions at the boundary

In this article we study the degenerate system (@r1,@r2>=0) subject to memory conditions on the boundary given [emailxa0protected]1(x)ut[emailxa0protected][emailxa0protected](u-v)[emailxa0protected]]0,+~[,@r2(x)vt[emailxa0protected]@a(u-v)[emailxa0protected]]0,+~[,[emailxa0protected]0,[emailxa0protected]!0^tg1(t-s)@[emailxa0protected][emailxa0protected](s)[emailxa0protected]1x]0,+~[,[emailxa0protected]0,[emailxa0protected]!0^tg2(t-s)@[emailxa0protected][emailxa0protected](s)[emailxa0protected]1x]0,+~[,(u(0),v(0))=(u^0,v^0)(@r1ut(0),@r2vt(0))=(@r1u^1,@r2v^1)[emailxa0protected],where @W is a bounded region in R^n whose boundary is partitioned into disjoint sets @C0, @C1. We prove that the dissipations given by the memory terms are strong enough to guarantee exponential (or polynomial) decay provided the relaxation functions also decay exponentially (or polynomially) and with the same rate of decay.

Global existence and uniform decay for the coupled Klein-Gordon-Schrödinger equations

Abstract. This paper is concerned to the existence, uniqueness and uniform decay for the solutions of the coupled Klein-Gordon-Schrödinger damped equations n

Intrinsic decay rates for the energy of a nonlinear viscoelastic equation modeling the vibrations of thin rods with variable density

ipsi_{t} + Deltapsi + i |psi|^{2}psi + igammapsi = -phipsiinOmega times (0,infty)

On existence and asymptotic stability of solutions of the degenerate wave equation with nonlinear boundary conditions

n

Geometrically constrained stabilization of wave equations with Wentzell boundary conditions

phi_{tt} - Deltaphi + mu^{2}phi + F(phi, phi_{t}) = beta |psi|^{2theta}inOmega times (0, infty)

Uniform Decay Rates for the Wave Equation with Nonlinear Damping Locally Distributed in Unbounded Domains with Finite Measure

where ω is a bounded domain of Rn, n≤ 3, F : R2→R is a C1-function; γ, β; θ are constants such that γ, β > 0 and 1 ≤ 2θ≤ 2.

Global Solvability and Asymptotic Stability for the Wave Equation with Nonlinear Boundary Damping and Source Term

Abstract We consider the long-time behavior of a nonlinear PDE with a memory term which can be recast in the abstract form d d u2062 t u2062 ρ u2062 ( u t ) + A u2062 u t u2062 t + γ u2062 A θ u2062 u t + A u2062 u - ∫ 0 t g u2062 ( s ) u2062 A u2062 u u2062 ( t - s ) = 0 ,

Uniform Decay Rates of Solutions to a Nonlinear Wave Equation with Boundary Condition of Memory Type

frac{d}{dt}rho(u_{t})+Au_{tt}+gamma A^{theta}u_{t}+Au-int_{0}^{t}g(s)Au(t% -s)=0,

Well-posedness and optimal decay rates for the wave equation with nonlinear boundary damping–source interaction

where A is a self-adjoint, positive definite operator acting on a Hilbert space H, ρ u2062 ( s )

Existence and uniform decay for a non‐linear viscoelastic equation with strong damping

{rho(s)}