Valéria N. Domingos Cavalcanti

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

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 ⁢ t ⁢ ρ ⁢ ( u t ) + A ⁢ u t ⁢ t + γ ⁢ A θ ⁢ u t + A ⁢ u - ∫ 0 t g ⁢ ( s ) ⁢ A ⁢ u ⁢ ( 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 ⁢ ( s )

Existence and decay rate estimates for the wave equation with nonlinear boundary damping and source term

{\rho(s)}

EXISTENCE AND ASYMPTOTIC STABILITY FOR EVOLUTION PROBLEMS ON MANIFOLDS WITH DAMPING AND SOURCE TERMS

is a continuous, monotone increasing function, and the relaxation kernel g ⁢ ( s )

Stabilization of the damped wave equation with Cauchy–Ventcel boundary conditions

{g(s)}

Intrinsic decay rate estimates for the wave equationwith competing viscoelastic and frictional dissipative effects

is a continuous, decreasing function in L 1 ⁢ ( ℝ + )

Decay of Solutions to Damped Korteweg–de Vries Type Equation

{L_{1}(\mathbb{R}_{+})}

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

with g ⁢ ( 0 ) > 0

HOMOGENIZATION AND UNIFORM STABILIZATION FOR A NONLINEAR HYPERBOLIC EQUATION IN DOMAINS WITH HOLES OF SMALL CAPACITY

{g(0)>0}