Azouz, SalimaGuesmia, Senoussi2018-07-312018-07-312018http://hdl.handle.net/123456789/4047In the present work we focus on the analysis of the asymptotic behaviour of the solutions to anisotropic singular perturbation boundary value problems. A complete description of the asymptotic behaviour on the whole domain of definition is established. Two types of functions are constructed. The first type acts far away from the boundary layers to give the best possible approximation. The second one deals with the behaviour near the boundary layers to recover the complete approximation with a sharper rate of convergence. In fact, we go beyond the limit behaviour by considering the regular and the composite asymptotic expansions of arbitrary order. This allows to get an asymptotic approximation of a polynomial rate of convergence in arbitrary order or even an exponential one.enSingular perturbationsLinear problemsBoundary layersThesis