In this paper, we study a complete second-order integro-differential operator equation in Hilbert space. The difference-type kernel of an integral perturbation is holomorphic semigroup bordered by unbounded operators. asymptotic behavior solutions studied. Asymptotic formulas for are proved the case when right-hand side close to almost periodic function. obtained applied problem forced longitud...

We present a control design method for nonlinear partial differential equations (PDEs) based on a combination of gain scheduling and backstepping theory for linear PDEs. A benchmark first-order hyperbolic system with an in-domain nonlinearity is considered first. For this system a nonlinear feedback law, based on gain scheduling, is derived explicitly, and a proof of local exponential stability...

A mathematical model has been developed and a numerical study of vapor bubble growth as result acoustic evaporation an encapsulated perfluorocarbon droplet in viscoelastic liquid is presented. The viscoelasticity the shell carrier taken into account according to Kelvin–Voigt rheological model. problem reduced solving system ordinary differential equations for radius temperature bubble, together...

The objective in this paper is to study a thermal frictional contact model. The deformable body consists of viscoelastic material and the process assumed be dynamic. It that behaves accordance with Kelvin-Voigt constitutive law effect added. variational formulation model leads coupled system including history-dependent hemivariational inequality for displacement fie...

Abstract Aimed towards an application of ultrasound diagnosis using contrast agents, the dynamics encapsulated bubbles has been theoretically investigated under restriction a single bubble. In this paper, we extend theory for bubble or some to that many bubbles, and investigate weakly nonlinear propagation in initially quiescent incompressible liquid, uniformly containing microbubbles by shell ...

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 ...

The wave propagation in viscothermoelastic materials is discussed the present work using nonlocal thermoelasticity model. This model was created Lord and Shulman generalized thermoelastic due to consequences of delay times formulations heat conduction motion equations. Eringen’s theory continuum. linear Kelvin–Voigt viscoelasticity explains viscoelastic properties isotropic material. analytical...

Abstract The paper presents a certain method of analysing the dynamics belt transmission. A flat transmission model developed by us was presented. For analysis, it assumed 5PK belt. discrete model, being system rigid beams interconnected with flexible and shock-absorbing elements, used. To account for mutual influence between pulleys, Kelvin–Voigt contact GMS friction also implemented, which al...

A thermodynamically consistent model for soft deformable viscoelastic magnets is formulated in actual space (Eulerian) coordinates. The possibility of a ferro-paramagnetic-type (or ferri-antiferromagnetic) transition exploiting the Landau phase-transition theory as well mechanical melting or solidification considered, being motivated and applicable to paleomagnetism (involving both thermo- isot...