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

Stéphane Malek

Abstract and Applied Analysis, 2017, vol. 2017, issue 1

Abstract: 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 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.

Date: 2017
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https://doi.org/10.1155/2017/9405298

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2017:y:2017:i:1:n:9405298

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