Moore-Gibson-Thompson thermoelasticity with two temperatures
R. Quintanilla
Abstract
In this note we propose the Moore-Gibson-Thompson heat conduction equation with two temperatures and prove the well posedness and the exponential decay of the solutions under suitable conditions on the constitutive parameters. Later we consider the extension to the Moore-Gibson-Thompson thermoelasticity with two temperatures and prove that we cannot expect for the exponential stability even in the one-dimensional case. This last result contrasts with the one obtained for the Moore-Gibson-Thompson thermoelasticity where the exponential decay was obtained. However we prove the polynomial decay of the solutions. The paper concludes by giving the main ideas to extend the theory for inhomogeneous and anisotropic materials.
Topics & Concepts
Exponential decayExtension (predicate logic)AnisotropyExponential functionThermal conductionPolynomialMathematicsHeat equationExponential stabilityMathematical analysisCalculus (dental)PhysicsThermodynamicsComputer scienceQuantum mechanicsNonlinear systemMedicineProgramming languageDentistryThermoelastic and Magnetoelastic PhenomenaNumerical methods in engineeringNumerical methods in inverse problems