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We consider a family of linear singularly perturbed PDE relying on a complex perturbation parameter $epsilon$. As in a former study of the authors (A. Lastra, S. Malek, Parametric Gevrey asymptotics for some nonlinear initial value Cauchy problems, J. Differential Equations 259 (2015), no. 10, 5220--5270), our problem possesses an irregular singularity in time located at the origin but, in the present work, it entangles also differential operators of Fuchsian type acting on the time variable. As a new feature, a set of sectorial holomorphic solutions are built up through iterated Laplace transforms and Fourier inverse integrals following a classical multisummability procedure introduced by W. Balser. This construction has a direct issue on the Gevrey bounds of their asymptotic expansions w.r.t $epsilon$ which are shown to bank on the order of the leading term which combines both irregular and Fuchsian types operators.
Analytic solutions and their formal asymptotic expansions for a family of the singularly perturbed $q-$difference-differential equations in the complex domain are constructed. They stand for a $q-$analog of the singularly perturbed partial differenti
We study a family of partial differential equations in the complex domain, under the action of a complex perturbation parameter $epsilon$. We construct inner and outer solutions of the problem and relate them to asymptotic representations via Gevrey
We consider semilinear stochastic evolution equations on Hilbert spaces with multiplicative Wiener noise and linear drift term of the type $A + varepsilon G$, with $A$ and $G$ maximal monotone operators and $varepsilon$ a small parameter, and study t
We consider singularly perturbed convection-diffusion equations on one-dimensional networks (metric graphs) as well as the transport problems arising in the vanishing diffusion limit. Suitable coupling condition at inner vertices are derived that gua
In this paper we consider the initial boundary value problem (IBVP) for the nonlinear biharmonic Schrodinger equation posed on a bounded interval $(0,L)$ with non-homogeneous Navier or Dirichlet boundary conditions, respectively. For Navier boundary