Fecha: 04/04/2012 11:00
Lugar: Seminario de Análisis Matemático y Didáctica de la Matemática
Grupo: GIR Análisis Funcional Aplicado
A q‐analog of a singularly perturbed Cauchy problem with irregular singularity in the complex domain is studied. Our result generalizes a previous result by S. Malek in . First, we construct solutions defined in open q‐spirals to the origin. Afterwards, we obtain the existence of a formal power series in the perturbation parameter which represents the solution and is the q‐Gevrey asymptotic expansion of the actual solutions. This is achieved by means of a q‐Gevrey version of Malgrange‐Sibuya theorem. (Joint work with Stéphane Malek.)  S. Malek, Singularly perturbed q‐difference‐differential equations with irregular singularity, J. Dynam. Control. Syst. 17 (2011),no.2.