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\textsc{Javier Sanz }
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(joint work with \textsc{A. Lastra} and \textsc{S. Malek})
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University of Valladolid, SPAIN\\[.5ex]
Email: \texttt{jsanzg@am.uva.es}
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{\bf Multi-level asymptotics for singularly perturbed linear
partial differential equations with ultraholomorphic
coefficients}
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 We study the asymptotic behavior of solutions to a family of singularly
 perturbed partial differential equations in the complex domain, with coefficients
admitting a representation in terms of elements of general ultraholomorphic
classes in a sector. These analytic solutions are asymptotically represented
by a formal power series in the perturbation parameter. The geometry of the
problem and the nature of the elements involved in it give rise to different
asymptotic levels, related to the so-called strongly regular sequences
defining the classes under consideration. The result, which generalizes a previous
one by A. Lastra and S. Malek \cite{LM1}, rests on a novel version of a multi-level
Ramis-Sibuya theorem and on the summability procedures introduced in \cite{LM2}.

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\bibitem{LM1} A. Lastra, S. Malek, {\it Multi-level Gevrey solutions of singularly perturbed linear partial differential equations}, submitted, available at http://arxiv.org/abs/1407.2008.

\bibitem{LM2} A. Lastra, S. Malek, J. Sanz, {\it Summability in general Carleman ultraholomorphic classes},
J. Math. Anal. Appl. (2015), http://dx.doi.org/10.1016/j.jmaa.2015.05.046.
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