216 research outputs found
Quasi-analyticity in Carleman ultraholomorphic classes
We give a characterization for two different concepts of quasi-analyticity in
Carleman ultraholomorphic classes of functions of several variables in
polysectors. Also, working with strongly regular sequences, we establish
generalizations of Watson's Lemma under an additional condition related to the
growth index of the sequence.Comment: To appear in Ann. Inst. Fourier, Grenobl
On Gevrey asymptotics for singularly perturbed difference-differential problems with an irregular singularity
We study a analog of a singularly perturbed Cauchy problem with irregular
singularity in the complex domain which generalizes a previous result by S.
Malek in \cite{malek}. First, we construct solutions defined in open
spirals to the origin. By means of a Gevrey version of Malgrange-Sibuya
theorem we show the existence of a formal power series in the perturbation
parameter which turns out to be the Gevrey asymptotic expansion (of certain
type) of the actual solutions.Comment: 30 page
On parametric Gevrey asymptotics for some Cauchy problems in quasiperiodic function spaces
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 Borel-Laplace
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 Ramis-Sibuya 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 Dirichlet-like series whose exponents are
positive real numbers which accumulate to the origin
On parametric Gevrey asymptotics for initial value problems with infinite order irregular singularity and linear fractional transforms
This paper is a continuation a previous work of the authors where parametric
Gevrey asymptotics for singularly perturbed nonlinear PDEs has been studied.
Here, the partial differential operators are combined with particular Moebius
transforms in the time variable. As a result, the leading term of the main
problem needs to be regularized by means of a singularly perturbed infinite
order formal irregular operator that allows us to construct a set of genuine
solutions in the form of a Laplace transform in time and inverse Fourier
transform in space. Furthermore, we obtain Gevrey asymptotic expansions for
these solutions of some order in the perturbation parameter
Gevrey multiscale expansions of singular solutions of PDEs with cubic nonlinearity
We study a singularly perturbed PDE with cubic nonlinearity depending on a
complex perturbation parameter . This is the continuation of a
precedent work by the first author. We construct two families of sectorial
meromorphic solutions obtained as a small perturbation in of two
branches of an algebraic slow curve of the equation in time scale. We show that
the nonsingular part of the solutions of each family shares a common formal
power series in as Gevrey asymptotic expansion which might be
different one to each other, in general
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