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Quasi-linear systems of PDE of first order with Cauchy data of higher codimensions. (English) Zbl 1316.35078

Summary: In this paper we discuss the local solvability of Cauchy problem for quasi-linear partial differential equations of first order. By using the classical method of characteristics we describe the non-uniqueness or the degree of freedom for solutions and also decide the conditions for the existence and the uniqueness of solutions for overdetermined systems of quasi-linear PDEs of first order.

MSC:

35F25 Initial value problems for nonlinear first-order PDEs
35A02 Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness
35N20 Overdetermined initial value problems for PDEs and systems of PDEs
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