Asymptotic behavior of reflection of discontinuities in thermoelasticity with second sound in one space variable
The authors consider an initial boundary value problem for the semilinear thermoelastic system with second sound in \(\{t, x > 0\}\). By using a technique introduced in [\textit{R. Racke}, Lectures on nonlinear evolution equations. Initial value problems. Aspects of Mathematics. 19. Braunschweig etc.: Vieweg (1992; Zbl 0811.35002)], they prove the existence of a local solution and the global existence of a small solution to the initial boundary value problem mentioned above under certain conditions on the growth rate of the nonlinear functions \((f,g)\) on the right-side of the mixed problem with respect to their arguments, provided that the initial data are smooth and satisfy some compatibility conditions. The attention of the authors is directed to the behavior of discontinuities of the solutions under the hypothesis that the problem has a solution in a time interval. In fact, the authors study the reflection of discontinuous waves on physical boundaries in thermoelasticity and to investigate the influence of physical coefficients of linearized thermoelastic operator on the asymptotic behavior of singularities.
scientific article; zbMATH DE number 5947384
scientific article