Summability in a monomial for some classes of singularly perturbed partial differential equation

Abstract

The aim of this paper is to continue the study of asymptotic expansions and summability in a monomial in any number of variables. In particular we characterize these expansions in terms of bounded derivatives and we develop tauberian theorems for the summability processes involved. Furthermore, we develop and apply the Borel-Laplace analysis in this framework to prove the monomial summability of solutions of a specific class of singularly perturbed PDEs.

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• Nonlinear evolution PDEs in R^+ \times C^d: existence and uniqueness of solutions, asymptotic and Borel summability
• An extension of Borel-Laplace methods and monomial summability
• Tauberian properties for monomial summability with applications to Pfaffian systems
• Tauberian theorems for $k$--summability with respect to an analytic germ
• Entire functions polynomially bounded in several variables

Cited by in corpus (1)

• Tauberian theorems for $k$--summability with respect to an analytic germ