Abstract
The solutions of finite-dimensional time-invariant transport equations are considered. With the aid of an auxiliary equation the given equation is shown to be equivalent to a pair of coupled linear equations. Further, any four distinct solutions of a transport equation are related to the solution of the auxiliary equation. For stationary processes with dimension one, this result reduces to that on the classic Riccati's equation. Results presented here are being generalized by R.M. Redheffer and the writer in an abstract space. However, this note points out some essential properties and some of the underlying methods without the abstract setting. To accomplish this goal we assume the system is finite dimensional and time-invariant. A one-dimensional example is given to illustrate the results.
Published Version
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