Abstract
The present paper concerns the study of travelling waves for the nonconservative model ut+(12u2)x=σx, σt+uσx=k2ux coming from elastodynamics. For this model, that does not admit nonconstant global smooth solutions, necessary and sufficient conditions for the propagation of distributional profiles are established. As an application we study the propagation of C1-profiles with one jump discontinuity. Surprisingly we also discover the possible developing of certain perturbations containing Dirac measures and also perturbations defined by distributions that are not measures. In all these cases the speed of propagation is evaluated. These results are obtained using a rigorous and consistent concept of a solution defined in the setting of a distributional product that is not constructed by approximation processes.
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