Galerkin-type solution for the Moore–Gibson–Thompson thermoelasticity theory - Singh B.; Mukhopadhyay S. (My University, 2025)
It is prominent that the Galerkin-type representation plays a dominant role in probing various challenges of mathematical physics, continuum mechanics and occupies an important place in the field of partial differential equations (PDEs). Thus, the contemporary analysis of different boundary value problems (BVPs) in thermoelasticity theory commonly begins by analyzing the Galerkin-type representation of the field equations in terms of elementary functions (harmonic, biharmonic, and metaharmonic, etc). This work is aimed at formulating the representation of a Galerkin-type solution by means of elementary functions for the recently developed Moore–Gibson–Thompson (MGT) thermoelasticity theory. The MGT theory is a generalized form of the Lord–Shulman (LS) model as well as of the Green–Naghdi (GN) thermoelastic model. Here, we establish a theorem and derive the Galerkin-type solution for the basic governing equations under this theory. Later, the Galerkin representation of a system of equations for steady oscillations is derived. Based on this representation, we finally establish the general solution (GS) for the system of homogeneous equations of stable oscillation, neglecting the extrinsic body force and extrinsic heat supply. © 2021, The Author(s), under exclusive licence to Springer-Verlag GmbH, AT part of Springer Nature.