On the well-posedness of the Green–Lindsay model

摘要

The present paper is devoted to an investigation of a nonclassical model for inhomogeneous anisotropic thermoelastic bodies with two constant relaxation times originally presented by Green and Lindsay. A variational formulation of the initial-boundary value problem corresponding to the linear dynamical three-dimensional Green–Lindsay model is applied. The corresponding spaces of vector-valued distributions with respect to the time variable with values in Sobolev spaces are defined and the existence and uniqueness of the solution in these spaces as well as continuous dependence of the solution on the given data is shown.