The Decoupling of Elastic Waves from a Weak Formulation Perspective

Abstract

Two weak formulations for the Lamé system with the boundary conditions of third and fourth types are proposed. It is shown that the regularity of the solutions and properties of the boundary surface guarantee the equivalence of variational and standard formulations of the problem. Moreover, if the boundary of $Ω$ is a Lipschitz polyhedron or if $\mathcal{S}$ ($x$) = 0 on $∂Ω$, the decoupling results of [8] are derived from the weak formulations.