Propagation of singularities in one-dimensional thermoelasticity. (English) Zbl 0910.73013
The authors study the Cauchy problem for the one-dimensional system of thermoelasticity, both for the linear homogeneous case and for the semilinear case. The aim is to investigate the propagation of singularities and the distribution of regular domains in the space-time region when the initial data have different regularity in different parts of the real line. It is found that the behaviour of characteristics is dominated by the hyperbolic part with exactly the same characteristic lines. The parabolic part due to the heat conduction introduces not only technical difficulties, but has also a deregularizing effect on the solution. The main arguments rely on a careful analysis in Fourier space and on the use of optimal regularity results for the heat conduction equation.
Reviewer: K.N.Srivastava (Bhopal)
MSC:
| 74B99 | Elastic materials |
| 35Q72 | Other PDE from mechanics (MSC2000) |
| 35L67 | Shocks and singularities for hyperbolic equations |
| 35K05 | Heat equation |
| 80A20 | Heat and mass transfer, heat flow (MSC2010) |
Keywords:
Cauchy problem; linear homogeneous case; semilinear case; behaviour of characteristics; hyperbolic part; parabolic part; deregularizing effect; Fourier space; optimal regularity resultsReferences:
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