Accession Number : AD0737305

Title :   The Scattering Theory of Lax and Phillips and Wave Propagation Problems of Classical Physics.

Descriptive Note : Technical summary rept., no. 16,

Corporate Author : UTAH UNIV SALT LAKE CITY DEPT OF MATHEMATICS

Personal Author(s) : LaVita,James A. ; Schulenberger,John R. ; Wilcox,Calvin H.

Report Date : DEC 1971

Pagination or Media Count : 43

Abstract : P. D. Lax and R. S. Phillips have developed an abstract theory of scattering for groups of unitary operators U(t) = exp(-it Lambda) acting on a Hilbert space and have applied it to various wave propagation problems for which Lambda is a partial differential operator. The scope of these applications has been limited by the assumptions that Lambda was elliptic and had smooth coefficients. In this paper it is shown how the abstract theory of Lax and Phillips can be applied to a class of nonelliptic operators Lambda with discontinuous coefficients. Examples include the equations for acoustic, electromagnetic and elastic waves in inhomogeneous media whose properties vary discontinuously. (Author)

Descriptors :   (*PARTIAL DIFFERENTIAL EQUATIONS, WAVE FUNCTIONS), (*WAVE PROPAGATION, THEOREMS), ELECTROMAGNETIC RADIATION, MECHANICAL WAVES, SCATTERING, SET THEORY

Subject Categories : Theoretical Mathematics
      Acoustics
      Optics
      Mechanics

Distribution Statement : APPROVED FOR PUBLIC RELEASE