A Dynamic Problem of Thermoelasticity

  • Jindřich Nečas

    Charles University, Prague, Czech Republic
  • Michael Růžička

    Albert-Ludwigs-Universität, Freiburg, Germany

Abstract

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 [5] and by J. Necas, A. Novotny and V. Sverak [6].

Cite this article

Jindřich Nečas, Michael Růžička, A Dynamic Problem of Thermoelasticity. Z. Anal. Anwend. 10 (1991), no. 3, pp. 357–368

DOI 10.4171/ZAA/456