Method of characteristics and first integrals for systems of quasi-linear partial differential equations of first order

Autor:	Chong-Kyu Han, Jong-Do Park
Rok vydání:	2014
Předmět:	Overdetermined system symbols.namesake Partial differential equation Method of characteristics General Mathematics Mathematical analysis First integrals symbols Quasi linear Vector field First order Frobenius theorem (differential topology) Mathematics
Zdroj:	Science China Mathematics. 58:1665-1676
ISSN:	1869-1862 1674-7283
DOI:	10.1007/s11425-014-4942-8
Popis:	Given a set of independent vector fields on a smooth manifold, we discuss how to find a function whose zero-level set is invariant under the flows of the vector fields. As an application, we study the solvability of overdetermined partial differential equations: Given a system of quasi-linear PDEs of first order for one unknown function we find a necessary and sufficient condition for the existence of solutions in terms of the second jet of the coefficients. This generalizes to certain quasi-linear systems of first order for several unknown functions.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::73d03baf161646e774daeb6689842069 https://doi.org/10.1007/s11425-014-4942-8 Zobrazit plný text záznamu Full text from SpringerLink