Abstract The final value problem for the Brinkman–Forchheimer–Kelvin–Voigt equations is analysed quadratic and cubic types of Forchheimer nonlinearity. main term in allowed to be fully anisotropic. It shown that solution depends continuously on data provided satisfies an a priori bound $$L^3.$$ L <m...

Abstract This paper investigates the transverse 3:1 internal resonance of an axially transporting nonlinear viscoelastic Euler-Bernoulli beam with a two-frequency parametric excitation caused by speed perturbation. The Kelvin-Voigt model is introduced to describe characteristics beam. governing equation and associated boundary conditions are obtained Newton’s second law. method multiple scales ...

u(x, 0) = u0(x) and ut(x, 0) = u1(x) for x ∈ Ω, and u(x, t)|∂Ω = 0, t ≥ 0, (1.2) where Ω is a bounded domain in R with smooth, say C-class, boundary ∂Ω and σ(|∇u|) is a function like σ = 1/ √ 1 + |∇u|2, mean curvature type nonlinearity. The viscosity term −∆ut is often called a Kelvin-Voigt type dissipation or strong dissipation which appears in phenomena of wave propagation in a viscoelastic m...

In classical tsunami-generation techniques, one neglects the dynamic sea bed displacement resulting from fracturing of a seismic fault. The present study takes into account these dynamic effects. Earth’s crust is assumed to be a Kelvin-Voigt material. The seismic source is assumed to be a dislocation in a viscoelastic medium. The fluid motion is described by the classical nonlinear shallow wate...

Abstract. In this paper we consider the transmission problem of a material composed of three components; one of them is a Kelvin–Voigt viscoelastic material, the second is an elastic material (no dissipation), and the third is an elastic material inserted with a frictional damping mechanism. The main result of this paper is that the rate of decay will depend on the position of each component. W...

The small-amplitude radial oscillations of a gas microbubble encapsulated by a viscoelastic solid shell and surrounded by a slightly compressible viscoelastic liquid are studied theoretically. The Kelvin–Voigt and 4-constant Oldroyd models are used to describe the viscoelastic properties of the shell and liquid, respectively. The equation for radial oscillation is derived using the method of ma...

In this paper initial boundary value problems, defined using quasilinear diffusion equations of Volterra type, are considered. These equations arise for instance to describe diffusion processes in viscoelastic media whose behaviour is represented by a Voigt-Kelvin model or a Maxwell model. We propose a finite difference discretization defined on a general nonuniform grid and we show second conv...