Opuscula Math. 25, no. 2 (2005), 299-306
On the structure of characteristic surfaces related with partial differential equations of first and higher orders. Part 1
Natalia K. Prykarpatska
Abstract. The geometric structure of characteristic surfaces related with partial differential equations of first and higher orders is studied making use the vector field technique on hypersurfaces. It is shown, that corresponding characteristics are defined uniquely up to some smooth tensor fields, thereby supplying additional information about the suitable set of their solutions. In particular, it may be very useful for studying asymptotic properties of solutions to our partial differential equations under some boundary conditions.
Keywords: characteristic surface, vector fields, tangency, Monge cone, tensor fields.
Mathematics Subject Classification: 34A30, 34B05, 35B12, 35A15, 35J50, 35J65, 46T15, 34B15.