Energy decay for a porous thermoelastic system with thermoelasticity of second sound and with a non-necessary positive definite energy

In this paper we investigate a porous thermoelastic system where the heat conduction is given by Cattaneo’s law and where the energy associated with the solution is not necessary positive definite (μξ=b2μξ=b2). We introduce a stability number χ and prove an exponential (resp. polynomial) decay result depending on χ.