 1012 Stephane MALEK
 On Gevrey asymptotics for some nonlinear integrodifferential equations
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Jan 18, 10

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Abstract. We construct formal power series solutions of nonlinear integrodifferential equations for given initial conditions which are holomorphic functions on a strip in the complex plane C. We give sufficient conditions on the shape of the equations and on the initial conditions under which there exist actual holomorphic solutions which are Gevrey asymptotic to the given formal series solutions with respect to the time variable on sectors in C. We get 1Gevrey asymptotic expansions on sectors of opening less than pi but not 1summability as it is the case for linear partial differential equations. Moreover, our approach yields global analytic solutions of these equations in both time and space variables.
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