The Scattering Theory of Lax and Phillips and Wave Propagation Problems of Classical Physics.
Technical summary rept., no. 16,
UTAH UNIV SALT LAKE CITY DEPT OF MATHEMATICS
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P. D. Lax and R. S. Phillips have developed an abstract theory of scattering for groups of unitary operators Ut 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
- Theoretical Mathematics
- Radiofrequency Wave Propagation