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∣   k   0) for k 0 ≥ 2 near the origin. The asymptotic behaviour of the solution as t → ∞ is also described.