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

Autor:	Chong-Kyu Han, Jae-Seong Cho
Rok vydání:	2002
Předmět:	Overdetermined system symbols.namesake Pure mathematics General Mathematics Existential quantification Compatibility (mechanics) Systems of partial differential equations Mathematical analysis symbols Prolongation Frobenius theorem (differential topology) Submanifold Mathematics
Zdroj:	Journal of the Korean Mathematical Society. 39:237-252
ISSN:	0304-9914
DOI:	10.4134/jkms.2002.39.2.237
Popis:	We study the compatibility conditions and the exis- tence of solutions for overdetermined PDE systems that admit com- plete prolongation. For a complete system of order k there exists a submanifold of the (k i1)st jet space of unknown functions that is the largest possible set on which the initial conditions of (k i 1)st order may take values. There exists a unique solution for any ini- tial 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 Pfaan dier- ential system associated with the complete prolongation.
Databáze:	OpenAIRE
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