Analysis of weak singularities of solutions to 1-D thermoelasticity (Q2759792)

The propagation of singularities of solutions to the Cauchy problem for the one-dimensional semilinear system of equations of thermoelasticity is examined . The local existence and regularity of solutions is proved under certain assumption of the smoothness of initial data. The main idea is that the weak singularities of the solution to the semilinear problem are dominated by the corresponding linear problem. New a priori estimates to the linear problem are obtained and then applied to the proof of the uniqueness and regularity of the semilinear problem. The proof uses the construction of solution sequences by the Picard iteration for the semilinear Cauchy problem.NEWLINENEWLINEFor the entire collection see [Zbl 0969.00056].