Analytical Methods for a Selection of Elliptic Singular Perturbation Problems.211 Modelling, Analysis and Simulation

摘要

The authors consider several model problems from a class of elliptic perturbation211u001eequations in two dimensions. The domains, the differential operators, the 211u001eboundary conditions, and so on, are rather simple, and are chosen in a way that 211u001ethe solutions can be obtained in the form of integrals or Fourier series. By 211u001eusing several techniques from asymptotic analysis (saddle point methods, for 211u001einstance) the authors try to construct asymptotic approximations with respect to 211u001ethe small parameter that multiplies the differential operator of highest order. 211u001eIn particular, the authors consider approximations that hold uniformly in the so-211u001ecalled boundary layers. The authors also pay attention to how to obtain a few 211u001eterms in the asmptotic expansion by using direct methods based on singular 211u001eperturbation methods.