In the present article, we consider a thermoelastic plate of Reissner-Mindlin-Timoshenko type with the hyperbolic heat conduction arising from Cattaneo’s law. In the absense of any additional mechanical dissipations, the system is often not even strongly stable unless restricted to the rotationally symmetric case, etc. We present a well-posedness result for the linear problem under general mixe...

In the paper we present a survey on the mathematical modeling of nonconvex and nonsmooth problems arising in the mathematical theory of contact mechanics which is a growing field in engineering and scientific computing. The approach to such problems is based on the notion of hemivariational inequality and our presentation focuses on three aspects. First we present the ideas leading to inequalit...

The Hyperbolic Heat Transfer Equation describes heat processes in which extremely short periods of time or extreme temperature gradients are involved. It is already known that there are solutions of this equation which exhibit a chaotic behaviour, in the sense of Devaney, on certain spaces of analytic functions with certain growth control. We show that this chaotic behaviour still appears when ...

The heat transport at microscale is vital important in the field of micro-technology. In this paper heat transport in a two-dimensional thin plate based on dual-phase-lagging (DPL) heat conduction model is investigated. The solution was obtained with the help of superposition techniques and solution structure theorem. . The whole analysis is presented in dimensionless form. A numerical example ...

The falling and settling of solid particles in gases and liquids is a natural phenomenon happens in many industrial processes. This phenomenon has altered pure forced convection to a combination of heat conduction and heat convection in a flow over a plate. In this paper, the coupling of conduction (inside the plate) and forced convection of a non-homogeneous nanofluid flow (over a flat plate) ...