Abstract:

The Thermoelastic equation of type Ⅲ defined on the outer region of a three-dimensional sphere is considered. It is assumed that the solution of the equation satisfies certain boundary conditions at the boundary of the sphere. By setting an arbitrary parameter greater than zero in the energy expression after making certain constraints on the boundary conditions, the fast growth rate or decay rate of the solution with the distance from the origin is obtained by using energy analysis method and differential inequality technology. In the case of decay, the continuous dependence of solutions on coefficients is proved.

Key words: Type Ⅲ thermoelastic equation, Decay rate, Growth rate, Continuous dependence