Opuscula Math. 25, no. 2 (2005), 299-306

 
Opuscula Mathematica

On the structure of characteristic surfaces related with partial differential equations of first and higher orders. Part 1

Natalia K. Prykarpatska
Marzena Pytel-Kudela

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.

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  • Natalia K. Prykarpatska
  • AGH University of Science and Technology, Faculty of Applied Mathematics, al. Mickiewicza 30, 30-059 Kraków, Poland
  • Marzena Pytel-Kudela
  • AGH University of Science and Technology, Faculty of Applied Mathematics, al. Mickiewicza 30, 30-059 Kraków, Poland
  • Received: 2005-02-18.
Opuscula Mathematica - cover

Cite this article as:
Natalia K. Prykarpatska, Marzena Pytel-Kudela, On the structure of characteristic surfaces related with partial differential equations of first and higher orders. Part 1, Opuscula Math. 25, no. 2 (2005), 299-306

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