Passive linear systems of partial differential equations

In this paper the concept of a system passive relative to a cone that was introduced by V. S. Vladimirov for the case of translation-invariant systems is extended to systems which are not translation invariant. For systems of linear partial differential equations of first order with variable coefficients necessary and sufficient conditions are found for them to be passive relative to a cone. A generalized Cauchy problem is posed for such systems, and it is proved that this problem is well posed under the condition of strict nondegeneracy.
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