In this paper we consider the following three-phase-lag thermoelastic plate: ρu¨=−Δ(μΔu−mθ),c(θ˙+τqθ¨)=mΔ(u˙+τqu¨)+Δ(k∗α+τν∗θ+kτθθ˙).We obtain analyticity and exponential stability for associated C0-semigroup when coefficients satisfy τν≥k∗τq. The of semigroup still holds τν<k∗τq. However, instability solution was proved by Routh–Hurwitz rule.

A semi-analytical investigation has been carried out to analyze unsteady MHD second-grade flow under the Dual-Phase-Lag (DPL) heat and mass transfer model in a vertical microchannel filled with porous material. Diffusion thermo (Dufour) effects and homogenous chemical reaction are considered as well. The governing partial differential equations are solved by using the Laplace transform method w...

the three-phase-lag model and green–naghdi theory without energy dissipation are employed to study the deformation of a two-temperature fiber-reinforced medium with an internal heat source that is moving with a constant speed under a hydrostatic initial stress and the gravity field.  the modulus of the elasticity is given as a linear function of the reference temperature. the exact expressions ...

In this paper, we propose a system of equations governing the dual-phase-lag heat conduction with microtemperatures. Several conditions on coefficients are imposed so that energy is positive definite and dissipative. On base prove well-posedness exponential stability by means semigroup theory frequency domain method.

the microstructure of dual phase steels can be considered as a matrix of ferrite phase reinforced by martensite particles. recent measurements show that the mechanical properties of the ferrite phase are changed with the distance from the martensite grains. in this paper, a new method has been proposed to consider this phenomenon in finite element modeling of dual phase steels microstructure. i...