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

• Autorzy: Prykarpatska N.K. , Pytel-Kudela M.
• Języki publikacji: EN

Abstrakty

EN

The geometric structure of characteristic surfaces related with partial differential equations of first and higer 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.

Słowa kluczowe

EN

characteristic surface; vector fields; tangency; Monge cone; tensor fields

• Wydawca: AGH University of Science and Technology Press
• Czasopismo: Opuscula Mathematica
• Rocznik: 2005
• Tom: Vol. 25, no. 2
• Strony: 299--306
• Opis fizyczny: Bibliogr. 9 poz.

Twórcy

autor

Prykarpatska N.K.

• AGH University of Science and Technology, Faculty of Applied Mathematics, al. Mickiewicza 30, 30-059 Kraków, Poland

autor

Pytel-Kudela M.

• AGH University of Science and Technology, Faculty of Applied Mathematics al. Mickiewicza 30, 30-059 Kraków, Poland

Bibliografia

• [1] Malgrange B.: Existence et approximation des solution des equations aux derivees partielles et des equations de convolution. Ann. Inst. Fouier, (6) 1956, 271—351.
• [2] Evans L.C.: Partial differential equations. AMB, USA, 1998.
• [3] Benton S.: The Hamilton-Jakobi equation: a global approach. Academic Press USA, 1977.
• [4] Garabedian P.: Partial differential equations. Wiley Publ., USA, 1964. [5] John F.: Partial differential equations. Berlin, Springer, 1970.
• [6] Arnold V. I.: Lectures on partial differential equations. Moscow, Fazis, 1999 (Rus­sian).
• [7] Prykarpatska N.K., Blackmore D.L., Prykarpatsky A.K., Pytel-Kudela M.: On the inf-type extremality solutions to Hamilton-Jacobi equations and some genera­lizations. Miskolc Mathematical Notes (4) 2003, 157-180.
• [8] Prykarpatska N.K., Prytula M.M.: On the inf-type extremality solution to a Hamilton-Jacobi equation on the sphere SN. Nonlinear Oscillations, (3) 2000 1, 74-77.
• [9] Mykytiuk Ya. V., Prykarpatsky A. K., Blackmore D.: The Lax solution to a Hamil-ton-Jacobi equation and its generalization. Nonlinear Analysis, (2003) 55, 629-640.