Vol. 30, No. 3, 1969

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Determination of hyperbolicity by partial prolongations

Harold H. Johnson

Vol. 30 (1969), No. 3, 679–695

In [3] it was shown that non-hyperbolic systems of partial differential equations may sometimes be altered by partial prolongations so they become hyperbolic. This paper solves two problems conceming this process for normal systems with two independent variables. First, if hyperbolicity is obtainable, it can be obtained after a bounded number of steps, the bound depending only on the algebraic structure of the given system and easily calculated. Second, an explicit procedure is described whereby any system which is absolutely equivalent to a hyperbolic system can be changed into a hyperbolic system. In addition much of the underlying algebraic structure of such systems and their partial prolongations is analyzed.

Mathematical Subject Classification
Primary: 35.57
Published: 1 September 1969
Harold H. Johnson