Estudo dun problema de perturbación singular para unha clase de inecuacións variacionais

Abstract

The main goal of this PhD thesis is to study the asymptotic behaviour of a degenerate singular perturbation problem for a class of nonlinear variational inequalities depending on a small positive parameter. These inequalities arise from the application of variational techniques to steady state diffusion problems related to different scientific areas. In addition to the nonlinearity, other remarkable contributions of this thesis are the inclusion of a boundary term and a degenerate function in the lower-order term, which induce changes in the behaviour of the solution when the small parameter goes to zero. Furthermore, the existence and uniqueness of solutions is analyzed, and several results about regularity and numerical approximation are introduced as well. A collection of examples for specific cases, distributed throughout each section, completes this memory and helps clarify the results obtained.