On Singular Solutions to PDEs with Turning Point Involving a Quadratic Nonlinearity

Stéphane Malek
2017 Abstract and Applied Analysis  
We study a singularly perturbed PDE with quadratic nonlinearity depending on a complex perturbation parameter ϵ. The problem involves an irregular singularity in time, as in a recent work of the author and A. Lastra, but possesses also, as a new feature, a turning point at the origin in C. We construct a family of sectorial meromorphic solutions obtained as a small perturbation in ϵ of a slow curve of the equation in some time scale. We show that the nonsingular parts of these solutions share
more » ... e solutions share common formal power series (that generally diverge) in ϵ as Gevrey asymptotic expansion of some order depending on data arising both from the turning point and from the irregular singular point of the main problem.
doi:10.1155/2017/9405298 fatcat:ufnjwacx3fd6lba6kpk7lhf34a