We consider a thermoelastic theory where the heat conduction is described by Moore–Gibson–Thompson equation. In fact, this equation can be obtained after introduction of relaxation parameter in Green–Naghdi type III model. analyse one- and three-dimensional cases. three dimensions, we obtain well-posedness stability solutions. one dimension, exponential decay instability solutions depending on conditions over system constitutive parameters. also propose possible extensions for these theories.

In this article, we use the Nunziato–Cowin theory of materials with voids to derive a thermoelastic solids, which have double porosity structure. The new is not based on Darcy's law. case equilibrium, in contrast classical elastic porosity, structure body influenced by displacement field. We prove uniqueness solutions means logarithmic convexity arguments as well instability whenever internal energy positive definite. Later, semigroup existence that positive. deformation an space spherical...

In this note we propose the Moore-Gibson-Thompson heat conduction equation with two temperatures and prove well posedness exponential decay of solutions under suitable conditions on constitutive parameters. Later consider extension to thermoelasticity that cannot expect for stability even in one-dimensional case. This last result contrasts one obtained where was obtained. However polynomial solutions. The paper concludes by giving main ideas extend theory inhomogeneous anisotropic materials.

The three-dual-phase-lag theory based on the constitutive law q(P, t + τ q ) = −(k∇T(P, T k∗∇ν(P, τν)), was proposed by Roy Choudhuri as an extension of Tzou where recent theories Greeen and Naghdi could be recover. Although it proposes a that compatible with our intuition, when we adjoin energy equation −∇q(x, t) c[Tdot](x, t), obtain ill-posed problem, is, problem which has sequence eigenvalues such their real part are positive (and go to infinity). A consequence this fact is always...

In this paper, we consider a thermoelastic model where heat conduction is described by the history dependent version of Moore–Gibson–Thompson equation, arising via introduction relaxation parameter in Green-Naghdi type III theory. The well-posedness resulting integro-differential system discussed. one-dimensional case, exponential decay energy proved.

We consider the system of dual-phase-lag thermoelasticity proposed by Chandrasekharaiah and Tzou. First, we prove that solutions problem are generated a semigroup quasi-contractions. Thus, third order in time is well-posed. Then exponential stability investigated. Finally spatial behavior analyzed semi-infinite cylinder result on domain influence obtained.

In this paper we obtain the existence of solutions and continuous dependence on supply terms initial conditions for equation dual-phase-lag heat conduction theory. When phase-lag constants satisfy a certain condition can prove exponential stability with respect to time spatial variables. is not satisfied instability solutions.

We investigate the equation of dual-phase-lag heat conduction proposed by Tzou. To describe this equation, we use phase lag flux and gradient temperature. analyse basic properties solutions problem. First, prove that when both parameters are positive, problem is well posed spatial decay controlled an exponential distance. When temperature bigger than flux, exponentially stable (which a natural property to expect for equation) behaviour square Also, uniqueness result unbounded proved in case.

<p>This research was concerned with a linear theory of thermoelasticity microtemperatures where the second thermal displacement gradient and are included in classical set independent constitutive variables. The master balance laws micromorphic continua, strain elasticity, Green-Naghdi thermomechanics were used to derive theory. semigroup operators allowed us prove that problem is well-posed. For equations isotropic rigids, we presented natural extension Cauchy-Kovalevski-Somigliana...