Journal of the Mathematical Society of Japan
- J. Math. Soc. Japan
- Volume 60, Number 2 (2008), 603-630.
Logarithmic singularities of solutions to nonlinear partial differential equations
We construct a family of singular solutions to some nonlinear partial differential equations which have resonances in the sense of a paper due to T.Kobayashi. The leading term of a solution in our family contains a logarithm, possibly multiplied by a monomial. As an application, we study nonlinear wave equations with quadratic nonlinearities. The proof is done by the reduction to a Fuchsian equation with singular coefficients.
J. Math. Soc. Japan, Volume 60, Number 2 (2008), 603-630.
First available in Project Euclid: 30 May 2008
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 35A20: Analytic methods, singularities
Secondary: 35L70: Nonlinear second-order hyperbolic equations
TAHARA, Hidetoshi; YAMANE, Hideshi. Logarithmic singularities of solutions to nonlinear partial differential equations. J. Math. Soc. Japan 60 (2008), no. 2, 603--630. doi:10.2969/jmsj/06020603. https://projecteuclid.org/euclid.jmsj/1212156664