The dynamic response of an initially flat viscoelastic membrane is investigated. The viscoelastic model is described with fractional order derivatives. The membrane is subjected to surface transverse and inplane dynamic loads. The governing equations are three coupled second order nonlinear partial FDEs (fractional differential equations) of hyperbolic type in terms of the displacement componen...

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.

The existence of a unique strong solution for the Cauchy problem to semilinear nondegenerate fractional differential equation and for the generalized Showalter–Sidorov problem to semilinear fractional differential equation with degenerate operator at the Caputo derivative in Banach spaces is proved. These results are used for search of solution existence conditions for a class of optimal contro...

Existence of a very weak solution to the d-dimensional thermo-viscoelasticity system for Kelvin-Voigt-type material at small strains involving (possibly nonlinear) monotone viscosity of a p-Laplacian type and temperature-dependent heat capacity of an (ω−1)-polynomial growth is proved by a successive passage to a limit in a suitably regularized Galerkin approximation and sophisticated a priori e...

This paper is on the asymptotic behavior of elastic string equation with localized degenerate Kelvin–Voigt damping u t ( x , ) − [ + b ] = 0 ∈ 1 > \begin{equation} u_{tt}(x,t)-[u_{x}(x,t)+b(x) u_{xt}(x,t) ]_{x}=0,\; x\in (-1,1),\; t>0, \end{equation} (0.1)where $b(x)=0$ $x\in (-1,0]$ and α $b(x)=x^\alpha >0$ (0,1)$ for $\alpha \in . It known that optimal decay rate solution 2 $t^{-2}$ in limit ...

The microscopic structure of a plant cell wall is given by cellulose microfibrils embedded in a cell wall matrix. In this paper we consider a microscopic model for interactions between viscoelastic deformations of a plant cell wall and chemical processes in the cell wall matrix. We consider elastic deformations of the cell wall microfibrils and viscoelastic Kelvin–Voigt type deformations of the...

In this paper, we apply the thermodynamic framework recently put into place by Rajagopal and co-workers, to develop rate-type models for viscoelastic fluids which do not possess instantaneous elasticity. To illustrate the capabilities of such models we make a specific choice for the specific Helmholtz potential and the rate of dissipation and consider the creep and stress relaxation response as...