Thermoelastic coupled Lamé equations with logarithmic nonlinearity and multiple time delays: Existence, uniqueness, and exponential stability

This paper investigates the well-posedness and asymptotic stability of a thermoelastic coupled Lamé system with logarithmic nonlinearity and time delays. The thermal effect is modeled via a Fourier-type heat equation with coupling satisfying the Onsager relations. Using semigroup theory and potential well methods, we establish local and global existence of weak solutions. Under enhanced damping conditions with thermal diffusion, we prove exponential decay of the total energy via a Lyapunov functional. This work significantly extends previous results by incorporating thermal dissipation alongside mechanical damping and delay, showing that the thermal effect enhances stability without affecting the potential well structure.