V.N. Domingos Cavalcanti

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

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

i\psi_{t} + \Delta\psi + i\ |\psi|^{2}\psi + i\gamma\psi = -\phi\psi\in\Omega \times (0,\infty)

Numerical analysis for the wave equation with locally nonlinear distributed damping

\phi_{tt} - \Delta\phi + \mu^{2}\phi + F(\phi, \phi_{t}) = \beta\ |\psi|^{2\theta}\in\Omega \times (0, \infty)

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

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.

Existence and uniform decay rates for viscoelastic problems with nonlinear boundary damping

Abstract We study the global existence of solutions of the nonlinear degenerate wave equation (ρ⩾0) (∗) ρ(x)y″−Δy=0 in Ω × ]0,∞[, y=0 on Γ 1 × ]0,∞[, ∂y ∂ν +y′+f(y)+g(y′)=0 on Γ 0 × ]0,∞[, y(x,0)=y 0 , ( ρ y′)(x,0)=( ρ y 1 )(x) in Ω, where y′ denotes the derivative of y with respect to parameter t, f(s)=C0|s|δs and g is a nondecreasing C1 function such that k1|s|ξ+2⩽g(s)s⩽k2|s|ξ+2 for some k1,k2>0 with 0 0 if n=1,2. The existence of solutions is proved by means of the Faedo–Galerkin method. Furthermore, when ξ=0 the uniform decay is obtained by making use of the perturbed energy method.

General decay rate estimates for viscoelastic dissipative systems

We study the global existence and uniform decay rates of solutions of the problem

Existence and Exponential Decay for a Kirchhoff–Carrier Model with Viscosity

\begin{array}{*{20}c} {(P)} & {\left\{ \begin{gathered} u_{tt} - \Delta u = \left| u \right|^\rho uin\Omega \times ]0, + \infty [ \hfill \\ u = 0on\Gamma _0 \times ]0, + \infty [ \hfill \\ \partial _\nu u + g\left( {u_t } \right) = 0on\Gamma _1 \times ]0, + \infty [ \hfill \\ u\left( {x,0} \right) = u^0 \left( x \right),u_t \left( {x,0} \right) = u^1 \left( x \right); \hfill \\ \end{gathered} \right.} \\ \end{array}