On the Holmgren–John uniqueness theorem for the wave equation with piecewise analytic coefficients

Ya. V. Kurylev

Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 22, Tome 203 (1992), pp. 113-136

Résumé

In this paper a uniqueness theorem is proved for the wave equation in the domain $Q^{2T}=\Omega\times(0,2T)$, where $\Omega$ is a piecewise analytic Riemannian manifold (Riemannian polyhedron). Initial data are assumed to be given on a part $\Gamma_0\times(0,2T)$ of the space-time boundary of the cylinder $Q^{2T}$, $\Gamma_0\in\partial\Omega$. The uniqueness of a weak solution is proved “in the large”, in a domain formed by the corresponding characteristics of the wave equation.