Vol. 39, No. 2, 1971

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Conditions for isomorphism in partial differential equations

Harold H. Johnson

Vol. 39 (1971), No. 2, 401–406

This paper studies systems of linear homogeneous p.d.e. in two independent variables with constant coefficients. For such systems powerful algebraic tools are available to obtain results which may indicate patterns for more general systems. Linear isomorphism is defined, and necessary and sufficient conditions for linear isomorphism between two systems are found. This result is obtained from the infinite prolongation of the systems, and two systems are isomorphic if and only if their infinite prolongations are isomorphic. One unexpected result is the important role played by lower-order coefficients which do not appear in such classical motions as ellipticity, hyperbolicity or characteristics. The classification problem for these p.d.e. is reduced to a problem in linear algebra involving a finite number of relations.

Mathematical Subject Classification 2000
Primary: 35G05
Received: 21 September 1970
Published: 1 November 1971
Harold H. Johnson