Exponential stability in linear heat conduction with memory: a semigroup approach

This paper is concerned with the asymptotic behavior in time of solutions to a linear problem arising in the theory of heat conduction with memory. In a rigid heat conductor obeying the Gurtin-Pipkin constitutive model for the heat flux, the energy balance leads to an hyperbolic, linear integro-differential equation. In spite of the presence of a convolution term, the homogeneous original problem, subject to initial-history conditions, is transformed into an autonomous system by a suitable choice of variables. By means of semigroup techniques the exponential decay of solutions is provided.