On Parametric Gevrey Asymptotics for Some Cauchy Problems in Quasiperiodic Function Spaces

摘要: We investigate Gevrey asymptotics for solutions to nonlinear parameter depending Cauchy problems with 2π-periodic coefficients, initial data living in a space of quasiperiodic functions. By means the Borel-Laplace summation procedure, we construct sectorial holomorphic which are shown share same formal power series as asymptotic expansion perturbation parameter. observe small divisor phenomenon emerges from nature and is origin type divergence this series. Our result rests on classical Ramis-Sibuya theorem asks prove that difference any two neighboring constructed satisfies some exponential decay. This done by an study Dirichlet-like whose exponents positive real numbers accumulate origin.