A theory of dissipative
operators has been developed and successfully applied by R. S. Phillips to the
Cauchy problem for hyperbolic and parabolic systems of linear partial differential
equations with time invariant coefficients. Our purpose is to show that the Cauchy
problem for another system of equations can be brought within the scope of this
theory. For this system of equations, we shall parallel the early work of Phillips on
dissipative hyperbolic systems. This system of equations is general enough to
include, as special cases, such equations as the one dimensional Schrödinger
equation and the fourth order equation describing the damped vibrations of a
rod.
Several of the results necessary to accomplish this task provide generalizations of
the work of A. R. Sims on secondary conditions for nonselfadjoint second order
ordinary differential operators.
