20 citations · 86 across the 50 of their papers we have counts for
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Formal Gevrey solutions -- in analytic germs -- for higher order holomorphic PDEs
Sergio A. Carrillo, Alberto Lastra
We consider a family of holomorphic PDEs whose singular locus is given by the zero set of an analytic map with . Our goal is to establish conditions for the existence a…
Summability of formal solutions for a family of generalized moment integro-differential equations
Alberto Lastra, Sławomir Michalik, Maria Suwińska
Generalized summability results are obtained regarding formal solutions of certain families of linear moment integro-differential equations with time variable coefficients. The mai…
Estimates of formal solutions for some generalized moment partial differential equations
Alberto Lastra, Sławomir Michalik, Maria Suwińska
Using increasing sequences of real numbers, we generalize the idea of formal moment differentiation first introduced by W. Balser and M. Yoshino. Slight departure from the concept…
On parametric Borel summability for linear singularly perturbed Cauchy problems with linear fractional transforms
Alberto Lastra, Stéphane Malek
We consider a family of linear singularly perturbed Cauchy problems which combines partial differential operators and linear fractional transforms. We construct a collection of hol…
Gevrey multiscale expansions of singular solutions of PDEs with cubic nonlinearity
Alberto Lastra, Stéphane Malek
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…
On multiscale Gevrey and q-Gevrey asymptotics for some linear q-difference differential initial value Cauchy problems
Alberto Lastra, Stephane Malek
We study the asymptotic behavior of the solutions related to a singularly perturbed q-difference-differential problem in the complex domain. The analytic solution can be splitted a…
Strongly regular multi-level solutions of singularly perturbed linear partial differential equations
Alberto Lastra, Stéphane Malek, Javier Sanz
We study the asymptotic behavior of the solutions related to a family of singularly perturbed partial differential equations in the complex domain. The analytic solutions are asymp…
On parametric multisummable formal solutions to some nonlinear initial value Cauchy problems
Alberto Lastra, Stephane Malek
We study a nonlinear initial value Cauchy problem depending upon a complex perturbation parameter whose coefficients depend holomorphically on near the origin in $\math…
On parametric Gevrey asymptotics for some Cauchy problems in quasiperiodic function spaces
Alberto Lastra, Stéphane Malek
We investigate Gevrey asymptotics for solutions to nonlinear parameter depending Cauchy problems with -periodic coefficients, for initial data living in a space of quasiperiodi…
On parametric Gevrey asymptotics for some nonlinear initial value Cauchy problems
Alberto Lastra, Stéphane Malek
We study a nonlinear initial value Cauchy problem depending upon a complex perturbation parameter with vanishing initial data at complex time and whose coefficients depen…
On parametric Gevrey asymptotics for singularly perturbed partial differential equations with delays
Alberto Lastra, Stéphane Malek
We study a family of singularly perturbed difference-differential equations in the complex domain. We provide sectorial holomorphic solutions in the perturbation parameter .…
On complex singularity analysis for some linear partial differential equations in
Alberto Lastra, Stéphane Malek, Catherine Stenger
We investigate the existence of local holomorphic solutions of linear partial differential equations in three complex variables whose coefficients are singular along an analyti…
On Gevrey asymptotics for singularly perturbed difference-differential problems with an irregular singularity
Alberto Lastra, Stéphane Malek
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}. Fir…