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Nonlinear Damped Timoshenko Systems with Second Sound - Global Existence and Exponential Stability (1811.01128v1)
Published 2 Nov 2018 in math.AP
Abstract: In this paper, we consider nonlinear thermoelastic systems of Timoshenko type in a one-dimensional bounded domain. The system has two dissipative mechanisms being present in the equation for transverse displacement and rotation angle - a frictional damping and a dissipation through hyperbolic heat conduction modelled by Cattaneo's law, respectively. The global existence of small, smooth solutions and the exponential stability in linear and nonlinear cases are established.