JournalsprimsVol. 33, No. 5pp. 801–811

Nonlinear Singular First Order Partial Differential Equations Whose Characteristic Exponent Takes a Positive Integral Value

  • Hideshi Yamane

    University of Tokyo, Japan
Nonlinear Singular First Order Partial Differential Equations Whose Characteristic Exponent Takes a Positive Integral Value cover
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Abstract

We consider nonlinear singular partial differential equations of the form (tDt–ρ(x))u = ta(x)+_G_2(x)(t, tDtu, u, D1u,...,Dnu). It has been proved by Gerard and Tahara that there exists a unique holomorphic solution with u(0, x) ≡ 0 if the characteristic exponent ρ(x) avoids positive integral values. In the present paper we consider what happens if ρ(x) takes a positive integral value at x=0. Genetically, the solution u(t, x) is singular along the analytic set {t=0, ρ(x) ∈ N*}, N*={1, 2,...}, and we investigate how far it can be analytically continued.

Cite this article

Hideshi Yamane, Nonlinear Singular First Order Partial Differential Equations Whose Characteristic Exponent Takes a Positive Integral Value. Publ. Res. Inst. Math. Sci. 33 (1997), no. 5, pp. 801–811

DOI 10.2977/PRIMS/1195145018