06-66 S. Malek

On the summability of formal solutions of non-linear partial differential equations with shrinkings (298K, postscript) Mar 13, 06

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Abstract. We investigate the existence and the Borel summability of formal power series in one variable with holomorphic coefficients, solutions to non-linear partial differential equations with shrinkings having non-Kowalevski type in the complex domain. Sufficient conditions are given in terms of the shape of the functional partial differential equations and initial conditions. Existence and asymptotic behaviour of local sectorial holomorphic solutions to these non-linear functional partial differential equations are obtained as byproduct. We apply the results to the study of asymptotic behaviour of solutions to some advanced-argument partial differential equations in a neighborhood of infinity

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