Logarithmic singularities of solutions to nonlinear partial differential equations
Analysis of PDEs
2014-09-24 v1
Abstract
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 by the reduction to a Fuchsian equation with singular coefficients.
Cite
@article{arxiv.math/0703870,
title = {Logarithmic singularities of solutions to nonlinear partial differential equations},
author = {Hidetoshi Tahara and Hideshi Yamane},
journal= {arXiv preprint arXiv:math/0703870},
year = {2014}
}