A survey of topics in analysis and partial differential equations II

Denise Huet (1)

1 IECL - Institut Élie Cartan de Lorraine

This paper is the result of investigations suggested by recent publications and completes D.Huet [33] and [34]. The topics, which are dealt with, concern some spaces of functions, and properties of solutions of linear and nonlinear, stationary and evoluton di fferential equations namely: existence, spectral properties, resonances, singular perturbations, boundary layers, inertal manifolds. The aim of this document, and of [33] and [34], is to be a useful reference for (youngs) researchers in mathematics and applied sciences.

Mots clés: Inertial manifolds; Spaces of functions; Evolution equations and systems; Elliptic equations; Schrödinger operator; Spectral theory; Singular perturbations; Internal and boundary layers

Domaines: Equations aux dérivées partielles [math.AP]; Analyse fonctionnelle [math.FA]

Denise Huet. A survey of topics in analysis and partial differential equations II. Journal of operators, 2013, 2013, pp.562963. ⟨10.1155/2013/562963⟩. ⟨hal-00725460⟩