Global existence for the three-dimensional thermoelastic equations of Type II

Qin, Yuming; Deng, Shuxian; Huang, Lan; Ma, Zhiyong; Su, Xiaoke

doi:10.1090/S0033-569X-10-01188-1

Authors: Yuming Qin, Shuxian Deng, Lan Huang, Zhiyong Ma and Xiaoke Su
Journal: Quart. Appl. Math. 68 (2010), 333-348
MSC (2000): Primary 35B35, 35M13, 35D30
DOI: https://doi.org/10.1090/S0033-569X-10-01188-1
Published electronically: February 19, 2010
MathSciNet review: 2663003
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Abstract: In this paper, we shall establish some global existence results for a 3D hyperbolic system arising from Green-Naghdi models of thermoelasticity of type II with a dissipative boundary condition for the displacement. The existence and exponential decay of energy for the linear problem has been solved by Lazzari and Nibbi, Journal of Mathematical Analysis and Applications, 338 (2008), 317–329. Furthermore, we shall establish the global existence of solutions to semilinear and nonlinear thermoelastic systems by using the semigroup approach.

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