Asymptotic behaviour of small solutions of singularly perturbed problems

EXISTENCE AND ASYMPTOTIC ANALYSIS OF SOLUTIONS OF SINGULARLY PERTURBED BOUNDARY VALUE PROBLEMS by

Analytical Approximation to Solutions of Singularly Perturbed Boundary Value Problems

In this paper, a computational method is presented for solving a class of nonlinear singularly perturbed two-point boundary value problems with a boundary layer at the left of the underlying interval. First a zeroth order asymptotic expansion for the solution of the given singularly perturbed boundary value problem is constructed. Then the reduced terminal value problem is solved analytically u...

Concentration of solutions for some singularly perturbed Neumann problems

In these notes we describe some methods for studying the asymptotic behavior of solutions to a class of singularly perturbed elliptic problems. We present first the case of concentration at single points, and then at sets of positive dimension.

Multiple Boundary Peak Solutions for Some Singularly Perturbed Neumann Problems

We consider the problem " 2 u ? u + f (u) = 0 in u > 0 in ; @u @ = 0 on @; where is a bounded smooth domain in R N , " > 0 is a small parameter and f is a superlinear, subcritical nonlinearity. It is known that this equation possesses boundary spike solutions such that the spike concentrates, as " approaches zero, at a critical point of the mean curvature function H(P); P 2 @. It is also known ...

Fem for Singularly Perturbed Problems

We consider the numerical approximation of singularly perturbed elliptic boundary value problems over non-smooth domains. We use a decomposition of the solution that contains a smooth part, a corner layer part and a boundary layer part. Explicit guidelines for choosing mesh-degree combinations are given that yield nite element spaces with robust approximation properties. In particular, we const...