Thermoelastic problem in the setting of dual-phase-lag heat conduction: existence and uniqueness of a weak solution (Q2038198)

The objective of this study was to prove the existence and uniqueness of a weak solution for an isotropic thermoelastic system, considering dual-phase-lag heat conduction where the lagging parameters \(\tau_{q}\) and \(\tau_{\theta}\) were assumed to be positive. To achieve this, the authors utilized Rothe's method and semidiscretization in time, along with an a priori estimate to demonstrate the convergence of Rothe functions to a weak solution. Additionally, they utilized the variational technique to prove the uniqueness of the solution. Overall, this paper presents a valuable contribution to the understanding of isotropic thermoelastic systems with dual-phase-lag heat conduction.