Vol. 18, No. 3, 1966

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Second order dissipative operators

J. D. Brooks

Vol. 18 (1966), No. 3, 423–436

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.

Mathematical Subject Classification
Primary: 35.31
Secondary: 47.10
Received: 27 April 1965
Published: 1 September 1966
J. D. Brooks