We study a family of singular perturbation problems of the kind inf { 1 ε ∫ Ω f(u, ε∇u, ερ) dx : ∫

Conditions for observability of a linearized smoothairgap induction machine model are examined, and limitations of any speed-sensorless observer scheme based on such a model are discussed. An approach for speed-sensorless flux estimation based on singular perturbation theory is developed. This approach relies on the natural time-scale separation between the electrical and mechanical dynamics of...

In this note we study the electron spectral weight of doped Mott insulators based on the 2D slave boson gauge field theory. The vertex correction with static gauge field is calculated in the second order perturbation theory. The vertex correction is found to be singular at low energy and requires nonperturbative treatments. PACS numbers: 74.20.Mn, 74.25.-q, Typeset using REVTEX 1

Blow-up in second and fourth order semi-linear parabolic partial differential equations (PDEs) is considered in bounded regions of one, two and three spatial dimensions with uniform initial data. A phenomenon whereby singularities form at multiple points simultaneously is exhibited and explained by means of a singular perturbation theory. In the second order case we predict that points furthest...

In this paper we consider the standard map and we study the invariant curve obtained by analytical continuation with respect to the perturbative parameter of the invariant circle of rotation number the golden mean corresponding to the case We show that if we consider the parameterization that conjugates the dynamics of this curve to an irrational rotation the domain of de nition of this conjuga...

The existence of travelling wave solutions to a haptotaxis dominated model is analysed. A version of this model has been derived in Perumpanani et al (1999) to describe tumour invasion, where diffusion is neglected as it is assumed to play only a small role in the cell migration. By instead allowing diffusion to be small, we reformulate the model as a singular perturbation problem, which can th...

Relaxation oscillations are periodic orbits of multiple time scale dynamical systems that contain both slow and fast segments. The slow-fast decomposition of these orbits is defined in the singular limit. Geometric methods in singular perturbation theory classify degeneracies of these decompositions that occur in generic one parameter families of relaxation oscillations. This paper investigates...

Perturbation bounds in numerical linear algebra are traditionally derived and expressed using norms. Norm bounds cannot reflect the scaling or sparsity of a problem and its perturbation, and so can be unduly weak. If the problem data and its perturbation are measured componentwise, much smaller and more revealing bounds can be obtained. A survey is given of componentwise perturbation theory in ...