Tokyo Journal of Mathematics

A Sharp Form of the Uniqueness of the Solution to Nonlinear Totally Characteristic Partial Differential Equations

Hidetoshi TAHARA

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Abstract

The paper deals with the following nonlinear partial differential equation $(t \partial/\partial t)^m u = F (t,x, \{(t \partial/\partial t)^j (\partial/\partial x)^{\alpha} u\}_{j+\alpha \leq m, j<m} )$ with $(t,x) \in \mathbb{C}^2$ in the complex domain. Under the assumption that the equation is of totally characteristic type, the uniqueness of the solution was first proved in [4]. The present paper gives a sharp form of this uniqueness theorem.

Article information

Source
Tokyo J. Math., Volume 31, Number 1 (2008), 195-202.

Dates
First available in Project Euclid: 27 August 2008

Permanent link to this document
https://projecteuclid.org/euclid.tjm/1219844832

Digital Object Identifier
doi:10.3836/tjm/1219844832

Mathematical Reviews number (MathSciNet)
MR2426803

Zentralblatt MATH identifier
1207.35014

Subjects
Primary: 35A20: Analytic methods, singularities
Secondary: 35A10: Cauchy-Kovalevskaya theorems 35G20: Nonlinear higher-order equations

Citation

TAHARA, Hidetoshi. A Sharp Form of the Uniqueness of the Solution to Nonlinear Totally Characteristic Partial Differential Equations. Tokyo J. Math. 31 (2008), no. 1, 195--202. doi:10.3836/tjm/1219844832. https://projecteuclid.org/euclid.tjm/1219844832


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References

  • R. Gérard and H. Tahara:, Singular nonlinear partial differential equations, Vieweg, 1996.
  • H. Tahara: Uniqueness of the solution of non-linear singular partial differential equations, J. Math. Soc. Japan, 48 (1996), 729–744.
  • H. Tahara: On the uniqueness theorem for nonlinear singular partial differential equations, J. Math. Sci. Univ. Tokyo, 5 (1998), 477–506.
  • H. Tahara, Uniqueness of the solution of nonlinear totally characteristic partial differential equations, J. Math. Soc. Japan, 57 (2005), 1045–1065.