On the {$L\sp 2$}-well posedness of an initial boundary value problem for the 3D linear elasticity

Abstract

In a recent paper, we analyzed the {$L\sp 2$}-well posedness of an initial boundary value problem (ibvp) for the two-dimensional system of the linear elasticity under the uniform Kreiss- Lopatinskii condition. The present work is devoted to studying the analog of this problem in the three-dimensional case, when the Majda-Osher's analysis cannot be applied. The well-posedness is achieved by constructing an everywhere smooth non-degenerate dissipative Kreiss symmetrizer of the ibvp: this is done by adapting to the present situation the techniques already implemented for the two-dimensional linear elasticity. Compared with the latter case, some further technical difficulties have to be accounted for.