EXPONENTIAL STABILITY IN VISCOELASTIC AND ELASTIC SYSTEMS WITH THERMAL MEMORY

Abstract

Some linear evolution problems arising in the three-di\-men\-sio\-naltheory of thermoviscoelasticity with memory are considered.Assuming mixed boundary conditions,the associated evolution systems are formulated in a history space setting.Making use of semigroup techniques, well-posedness results are discussed,as well as asymptotic behavior of the solutions. When mechanical and thermalmemory kernels decay exponentially, the longtime behavior of solutions is provedto be of the same type.Restrictingour attention to a one-dimensional solid, the same decay is proved for alinearized thermoelastic model based on the Gurtin-Pipkin heat conduction law.