18-72 Alberto Lastra, Stephane Malek

On parametric Gevrey asymptotics for some initial value problems in two asymmetric complex time variables (715K, pdf) Jun 15, 18

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Abstract. We study a family of nonlinear initial value partial differential equations in the complex domain under the action of two asymmetric time variables. Different Gevrey bounds and multisummability results are obtained depending on each element of the family, providing a more complete picture on the asymptotic behaviour of the solutions of PDEs in the complex domain in several complex variables. The main results lean on a fixed point argument in certain Banach spaces in the Borel plane, together with a Borel summability procedure and the action of different Ramis-Sibuya theorems.

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