Journal of the Mathematical Society of Japan

Uniqueness of the solution of nonlinear totally characteristic partial differential equations

Hidetoshi TAHARA

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Abstract

Let us consider the following nonlinear singular partial differential equation ( t / t ) m u = F ( t , x , { ( t / t ) j ( / x ) α u } j + α m , j < m ) in the complex domain with two independent variables ( t , x ) C 2 . When the equation is of totally characteristic type, this equation was solved in [2] and [9] under certain Poincaré condition. In this paper, the author will prove the uniqueness of the solution under the assumption that u ( t , x ) is holomorphic in { ( t , x ) C 2 ; 0 < | t | < r , | arg t | < θ , | x | < R } for some r > 0 , θ > 0 , R > 0 and that it satisfies u ( t , x ) = O ( | t | a ) (as t 0 ) uniformly in x for some a > 0 . The result is applied to the problem of removable singularities of the solution.

Article information

Source
J. Math. Soc. Japan, Volume 57, Number 4 (2005), 1045-1065.

Dates
First available in Project Euclid: 14 June 2006

Permanent link to this document
https://projecteuclid.org/euclid.jmsj/1150287303

Digital Object Identifier
doi:10.2969/jmsj/1150287303

Mathematical Reviews number (MathSciNet)
MR2183583

Zentralblatt MATH identifier
1163.35302

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

Keywords
uniqueness of the solution nonlinear PDE totally characteristic PDE

Citation

TAHARA, Hidetoshi. Uniqueness of the solution of nonlinear totally characteristic partial differential equations. J. Math. Soc. Japan 57 (2005), no. 4, 1045--1065. doi:10.2969/jmsj/1150287303. https://projecteuclid.org/euclid.jmsj/1150287303


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References

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