Variational principle and continuous dependence results on the generalized poro-thermoelasticity theory with one relaxation parameter

Abstract

The present work is devoted to a study of the generalized poro-thermoelasticity theory and aims to derive the variational principle and continuous dependence results in the context of this theory. The basic field equations are considered for an isotropic and homogeneous fluid-saturated poro-thermoelastic medium. With the concept of incorporating initial conditions into the field equations, an alternative characterization of the present mixed initial-boundary value problem is presented. By taking into account of this alternative characterization, a convolution type variational principle is derived in the context of this generalized poro-thermoelasticity theory. Further, a continuous dependence result of solution on initial data and external supply terms (heat source and body force) is established. Uniqueness of solution of the present problem is also shown to be followed from this result. © 2022, The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.