Rate of attraction for a semilinear thermoelastic system with variable coefficients
In this paper the authors consider a family of one-dimensional semilinear thermoelastic problems. Thermal conductivity and elasticity depend on a parameter ``epsilon'' assumed small. Each one of the problems has its global attractor which depends on the parameter. The aim of the paper is to obtain an estimate of the distance between the attractor (depending on the parameter) and the limit corresponding to the case that the parameter vanishes. The authors prove that this distance can be estimated by means of the norm in the \(L^p\)-space (``\(p\)'' greater or equal to two) of the differences between the elasticities and the thermal conductivities. To obtain the results the authors study the resolvents of the linear operators to clarify the rate of convergence of the semigropus as well as the rate of convergence of the equilibria and of the linearizations.
scientific article