On the transient acoustic scattering by a flat object

This paper deals with the transient acoustic scattering in the particular geometry of a flat objet (crack) inR3. The boundary integral for the “crack opening displacement” is studied as a spatial pseudo-differential equation with the frequency variable as a parameter. Existence, Uniqueness and Continuous dependence of the solution with respect to the data are obtained in the framework of Sobolev spaces of causal functions.

[1]  W. Rudin.  Real and complex analysis , 1968 .

[2]  F. Trèves.  Basic Linear Partial Differential Equations , 1975 .

[3]  Richard Paul Shaw,et al.  Comments on “Numerical Solution for Transient Scattering from a Hard Surface of Arbitrary Shape—Retarded Potential Technique“ [K. M. Mitzner, J. Acoust. Soc. Am. 42, 391–397 (1967)] , 1968 .

[4]  J. Lions,et al.  Non-homogeneous boundary value problems and applications , 1972 .

[5]  Brian Hiroyuki Sako.  A model for the crack and punch problem in elasticity , 1986 .

[6]  Richard Paul Shaw,et al.  Transient acoustic scattering by a free (pressure release) sphere , 1972 .

[7]  A. Bamberger et T. Ha Duong,et al.  Formulation variationnelle espace‐temps pour le calcul par potentiel retardé de la diffraction d'une onde acoustique (I) , 1986 .

[8]  H. Mieras,et al.  Time domain integral equation solution for acoustic scattering from fluid targets , 1981 .

[9]  L. Schwartz.  Théorie des distributions , 1966 .

[10]  Jacques Chazarain,et al.  Introduction à la théorie des équations aux dérivées partielles linéaires , 1981 .

[11]  J. Nédélec,et al.  Integral equations with non integrable kernels , 1982 .

[12]  A. Bamberger et T. Ha Duong,et al.  Formulation variationnelle pour le calcul de la diffraction d'une onde acoustique par une surface rigide , 1986 .

[13]  K. Mitzner,et al.  Numerical Solution for Transient Scattering from a Hard Surface of Arbitrary Shape—Retarded Potential Technique , 1967 .