Unique Global Solvability for¶Initial-Boundary Value Problems¶in One-Dimensional Nonlinear Thermoviscoelasticity
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- Watson, S. Arch. Rational Mech. Anal. (2000) 153: 1. doi:10.1007/s002050050007
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The balance laws of mass, momentum and energy are considered for a broad class of one-dimensional nonlinear thermoviscoelastic materials. For the initial-boundary value problem corresponding to pinned endpoints held at constant temperature, we establish existence and uniqueness of temporally global classical solutions for initial data of unrestricted size. Our approach also applies to all boundary conditions involving pinned or stress-free endpoints which are either held at constant temperature or insulated. An additional and novel feature of the theory is that solid-like and gaseous materials are treated in a unified way.