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Logarithmic singularities of solutions to nonlinear partial differential equations

Hidetoshi Tahara·Hideshi Yamane
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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.

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Hidetoshi Tahara, Hideshi Yamane. 2007-03-29. Logarithmic singularities of solutions to nonlinear partial differential equations. https://arxiv.org/abs/math/0703870

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