Global existence and uniqueness of smooth solutions is proven for the Cauchy problem of a coupled thermo-viscoelastic system with viscous, capillary, and thermal terms under small-data assumptions.
Andrews,On the existence of solutions to the equationutt =u xxt +σ(u x)x, J
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Global Smooth Solutions to a Thermoelastic Cauchy Problem in Phase Transitions
Global existence and uniqueness of smooth solutions is proven for the Cauchy problem of a coupled thermo-viscoelastic system with viscous, capillary, and thermal terms under small-data assumptions.