Author(s)： Lev Ivlev, Gaven J. Martin, Boris Pavlov and Larissa Petrova

J. Math-for-Ind. 4B (2012) 141-153.

• File： JMI2012B-9.pdf (866KB)

Abstract
We present spectral and scattering theories for a differential operator with a dissipation term that can be used to describe the dynamics of a tectonic plate with dissipative boundary conditions. The generating operator is non-selfadjoint causing some additional complexity. This difficulty has been overcome by developing the selfadjoint-dilation theory. We develop a functional model for the dissipative operator and the associated scattering theory of Lax-Phillips type.

Keyword(s).　 scattering theory, tectonic plate, dissipative boundary conditions, selfadjoint-dilation theory, spectrum