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

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<jats:title>Abstract</jats:title><jats:p>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∣<jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/tex2gif-sup-1.gif" xlink:title="urn:x-wiley:01704214:media:MMA1670150402:tex2gif-sup-1" />) for <jats:italic>k</jats:italic><jats:sub>0</jats:sub> ≥ 2 near the origin. The asymptotic behaviour of the solution as <jats:italic>t</jats:italic> → ∞ is also described.</jats:p>

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