# COMPLETE PROLONGATION AND THE FROBENIUS INTEGRABILITY FOR OVERDETERMINED SYSTEMS OF PARTIAL DIFFERENTIAL EQUATIONS

• Cho, Jae-Seong (Department of Mathematics, University of Illinois) ;
• Han, Chong-Kyu (Department of Mathematics, Seoul National University)
• Published : 2002.03.01
• 125 8

#### Abstract

We study the compatibility conditions and the existence of solutions or overdetermined PDE systems that admit complete prolongation. For a complete system of order k there exists a submanifold of the ($\kappa$-1)st jet space of unknown functions that is the largest possible set on which the initial conditions of ($\kappa$-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 system;integrability

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#### Cited by

1. Local embeddability of CR manifolds into spheres vol.344, pp.1, 2009, https://doi.org/10.1007/s00208-008-0302-8
2. SOLVABILITY OF OVERDETERMINED PDE SYSTEMS THAT ADMIT A COMPLETE PROLONGATION AND SOME LOCAL PROBLEMS IN CR GEOMETRY vol.40, pp.4, 2003, https://doi.org/10.4134/JKMS.2003.40.4.695