Removable singularities of solutions of nonlinear singular partial differential equations

• Autorzy: Hidetoshi Tahara
• Języki publikacji: EN

Abstrakty

EN

1. Introduction. The study of singularities has been one of the main subjects of research in partial differential equations. In the case of linear equations the singularities are now pretty well understood; but in the nonlinear case there seems to be still very few studies. In this paper I want to discuss the singularities of solutions of a class of nonlinear singular partial differential equations in the complex domain. The class is only a model, but it helps one understand that the situation in the nonlinear case is more complicated than in the linear case.

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 1996
• Tom: 33
• Numer: 1
• Strony: 395-399

Daty

wydano

1996

Twórcy

autor

Hidetoshi Tahara

• Department of Mathematics, Sophia University, Kioicho, Chiyoda-ku, 102 Tokyo, Japan

Bibliografia

• [1] R. Gérard and H. Tahara, Holomorphic and singular solutions of nonlinear singular first order partial differential equations, Publ. RIMS, Kyoto Univ. 26 (1990), 979-1000.
• [2] R. Gérard and H. Tahara, Solutions holomorphes et singulières d'équations aux dérivées partielles singulières non linéaires, Publ. RIMS, Kyoto Univ. 29 (1993), 121-151.
• [3] R. Gérard and H. Tahara, Formal, holomorphic and singular solutions of nonlinear singular partial differential equations, to appear.
• [4] T. Ishii, On propagation of regular singularities for nonlinear partial differential equations, J. Fac. Sci. Univ. Tokyo 37 (1990), 377-424.
• [5] H. Tahara, Fuchsian type equations and Fuchsian hyperbolic equations, Japan. J. Math. 5 (1979), 245-347.
• [6] H. Tahara, Fundamental systems of analytic solutions of Fuchsian type partial differential equations, Funk. Ekvac. 24 (1981), 135-140.
• [7] H. Tahara, Uniqueness of the solution of nonlinear singular partial differential equations, J. Math. Soc. Japan 48 (1996), to appear.