 1415 Alberto Lastra, Stephane Malek
 On parametric Gevrey asymptotics for some Cauchy problems in quasiperiodic function spaces
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Mar 19, 14

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Abstract. We investigate Gevrey asymptotics for solutions to nonlinear parameter depending Cauchy problems with periodic coefficients, for initial data living in a space of quasiperiodic functions. By means of the BorelLaplace summation procedure, we construct sectorial holomorphic solutions which are shown to share the same formal power series as asymptotic expansion in the perturbation parameter. We observe a small divisor phenomenon which emerges from the quasiperiodic nature of the
solutions space and which is the origin of the Gevrey type divergence of this formal series. Our result rests on the classical RamisSibuya theorem which asks to prove that the difference of any two neighboring constructed solutions satisfies some exponential decay. This is done by an asymptotic study of a Dirichletlike series whose exponents are positive real numbers which accumulate to the origin.
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