Global solution to the Cauchy problem in non-linear hyperbolic thermoelasticity

We prove the existence of global solutions for small data to the initial value problem for the non-linear hyperbolic system of partial differential equations describing a thermoelastic medium in a three-dimensional space under the assumption that the coefficients in the non-linear terms are smooth functions of their arguments and behave like 0(∣η∣) for k₀ ≥ 2 near the origin. The asymptotic behaviour of the solution as t → ∞ is also described.