Wave scattering by an elastic obstacle with interior cuts

• Autores: Luis P. Castro, David Natroshvili, Ioannis G. Stratis
• Localización: Mathematische Nachrichten, ISSN 0025-584X, Vol. 280, Nº. 9-10, 2007, págs. 996-1013
• Idioma: inglés
• DOI: 10.1002/mana.200510531
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• Resumen

  • We consider the direct interaction problem describing the scattering of acoustic waves by an elastic obstacle with interior cracks. By the potential method we reduce the problem to an equivalent system of integral (pseudodifferential) equations and study its solvability. In particular, we formulate necessary and sufficient conditions for the solvability in terms of the so-called Jones modes. We show that the direct scattering problem is solvable for arbitrary values of the frequency parameter and for arbitrary incident wave functions if the crack surface is traction free. We also investigate the regularity of the displacement field, and analyze the stress singularities at the crack edge