16-93 Stephane Malek

On singular solutions to PDEs with turning point involving a quadratic nonlinearity (599K, pdf) Nov 25, 16

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Abstract. We study a singularly perturbed PDE with quadratic nonlinearity depending on a complex perturbation parameter. The problem involves an irregular singularity in time, as in a previous work of the author and A. Lastra, but possess also, as a new feature, a turning point at the origin in the complex domain. We construct a family of sectorial meromorphic solutions obtained as a small perturbation in the parameter of a slow curve of the equation in some time scale. We show that the non singular part of these solutions share a common formal power series (that generally diverge) in the parameter as Gevrey asymptotic expansion of some order depending on data both arising from the turning point and from the irregular singular point of the main problem.

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