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Blow-up in nonlinear three-dimensional thermoelasticity. (English) Zbl 0705.35081
It is shown that solutions of the equations of nonlinear thermoelasticity in general will develop singularities in finite time: There are singularities for which no global \(C^ 2\)-plane wave solution exists. The idea is to transfer the classical linear decomposition of the displacement vector into a curl-free and a divergence-free part resp. to the nonlinear equation.
Reviewer: R.Racke

MSC:
35L67 Shocks and singularities for hyperbolic equations
74B20 Nonlinear elasticity
35Q72 Other PDE from mechanics (MSC2000)
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