J. Korean Math. Soc. 2002; 39(2): 237-252
Printed March 1, 2002
Copyright © The Korean Mathematical Society.
Jae-Seong Cho and Chong-Kyu Han
University of Illinois and Seoul National University
We study the compatibility conditions and the existence of solutions for overdetermined PDE systems that admit complete prolongation. For a complete system of order $k$ there exists a submanifold of the $(k-1)$st jet space of unknown functions that is the largest possible set on which the initial conditions of $(k-1)$st order may take values. There exists a unique solution for any initial condition that belongs to this set if and only if the complete system satisfies the compatibility conditions on the initial data set. We prove by applying the Frobenius theorem to a Pfaffian differential system associated with the complete prolongation.
Keywords: prolongation, overdetermined systems, integrability
MSC numbers: 35N10, 58A17
1997; 34(4): 771-790
2000; 37(2): 225-243
2003; 40(4): 695-708
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