The capillary traction of a liquid contact line causes highly localized deformations in soft solids, tremendously slowing down wetting and dewetting dynamics by viscoelastic braking. Enforcing nonetheless large velocities leads to the so-called stick-slip instability, during which periodically depins from its own ridge. mechanism this periodic motion and, especially, role fluid have remained el...

Mechanical properties of biological tissues are of interest for assessing the performance of elastographic methods that evaluate the stiffness characteristics of tissue. The mechanical properties of interest include the frequency-dependent complex moduli, storage and loss moduli of tissues. Determination of the mechanical properties of biological tissues is often limited by proper geometry of t...

Abstract We present models for convection in a mixture of viscous fluids when the layer is heated from below and simultaneously pointwise volume concentration one heavier below. This configuration produces problem competitive double diffusion since heating promotes instability, but greater density fluid stabilizing. The are linear type which may contain Kelvin–Voigt terms, gradients due to appe...

Abstract We present numerical techniques for calculating instability thresholds in a model thermal convection complex viscoelastic fluid of Kelvin–Voigt type. The theory presented is valid various orders an exponential fading memory term, and the strategy obtaining neutral curves discussed general case. Specific results are order zero, also known as Navier–Stokes–Voigt fluid, fluids 1 2. For la...

We study the robust output regulation of linear boundary control systems by constructing extended systems. The are established based on solving static differential equations under two new conditions. We first consider abstract setting and present finite-dimensional reduced order controllers. controller design is then used for particular PDE models: high-dimensional ...

This paper presents responses of an edge circular cantilever beam under the effect of an impact force. The beam is excited by a transverse triangular force impulse modulated by a harmonic motion. The Kelvin-Voigt model for the material of the beam is used. The cracked beam is modelled as an assembly of two sub-beams connected through a massless elastic rotational spring. The considered problem ...

We study the energy decay rate of Kelvin–Voigt damped wave equation with piecewise smooth damping on multi-dimensional domain. Under suitable geometric assumptions support damping, we obtain optimal polynomial which turns out to be different from one-dimensional case studied in Liu and Rao [Z. Angew. Math. Phys. 56 (2005), no. 4, 630–644]. This is saturated by high quasi-modes localized optics ...

The presence of a delay in thermoelastic system destroys the well-posedness and stabilizing effect heat conduction [1]. To avoid this problem, we add to system, at delayed equation, Kelvin–Voigt damping. At first, prove by semigroup theory. Next, under appropriate assumptions, exponential stability introducing suitable Lyapunov functional.