For a family of two-time singularly perturbed PDEs, the analytic solution decomposes into a convergent part plus two parts with Gevrey asymptotic orders 1/k1 and 1/k2 in the perturbation parameter.
Balser,Multisummability of formal power series solutions of partial differential equations with constant coefficients.J
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Parametric formal Gevrey asymptotic expansions in two complex time variable problems
For a family of two-time singularly perturbed PDEs, the analytic solution decomposes into a convergent part plus two parts with Gevrey asymptotic orders 1/k1 and 1/k2 in the perturbation parameter.