Zeitschrift für Analysis und ihre Anwendungen
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Published online: 1991-09-30
A Dynamic Problem of ThermoelasticityJindřich Nečas and Michael Růžička (1) Charles University, Prague, Czech Republic
(2) Albert-Ludwigs-Universität, Freiburg, Germany
A space-periodic problem of nonlinear thermoelasticity is considered. For an elastic, linear, isotropic, homogeneous, nonviscous body in small geometry, we obtain a nonlinear system of equations. For small coefficient of the heat extension a we find a time-global weak solution of the initial-value problem. The smallness of a is independent of the length of the time interval and of the datas. The space periodicity of the solution is related to the absence of reflected waves. A mixed problem for a bounded domain, even with a smooth boundary, seems to be an open problem. Our work is closely related to that by J. Necas  and by J. Necas, A. Novotny and V. Sverak .
Keywords: Global solutions, a priori estimates
Nečas Jindřich, Růžička Michael: A Dynamic Problem of Thermoelasticity. Z. Anal. Anwend. 10 (1991), 357-368. doi: 10.4171/ZAA/456