The Scattering Theory of Lax and Phillips and Wave Propagation Problems of Classical Physics.
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)
Document Details
- Document Type
- Technical Report
- Publication Date
- Dec 01, 1971
- Accession Number
- AD0737305
Entities
People
- Calvin H. Wilcox
- James A. Lavita
- John R. Schulenberger
Organizations
- University of Utah