The outgoing time-harmonic elastic wave in a half-plane with free boundary*

Mario Durán, Ignacio Muga, Jean Claude Nédélec

Research output: Contribution to journalArticlepeer-review

5 Scopus citations


Under a time-harmonic assumption, we prove existence and uniqueness results for the outgoing elastic wave in an isotropic half-plane, where the source is given by a local normal stress excitation of the free boundary. This is the starting point for problems of elastic wave scattering by locally perturbed flat surfaces. The main difficulty is that the free boundary condition induces the propagation of a Rayleigh surface wave guided by the unbounded flat frontier. Due to the presence of this surface wave in the far field expansion, we need to impose a new radiation condition in order to describe both volume and surface outgoing wave behavior and to show uniqueness.

Original languageEnglish
Pages (from-to)443-464
Number of pages22
JournalSIAM Journal on Applied Mathematics
Issue number2
StatePublished - 2011


  • Half-plane
  • Linear elasticity
  • Radiation condition
  • Rayleigh wave
  • Uniqueness


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