A singular perturbation approach to nonlinear shell theory

A nonlinear singular perturbation problem

Let F (uε) + ε(uε − w) = 0 (1) where F is a nonlinear operator in a Hilbert space H, w ∈ H is an element, and ε > 0 is a parameter. Assume that F (y) = 0, and F ′(y) is not a boundedly invertible operator. Sufficient conditions are given for the existence of the solution to (1) and for the convergence limε→0 ‖uε−y‖ = 0. An example of applications is considered. In this example F is a nonlinear ...

Singular perturbation theory

When we apply the steady-state approximation (SSA) in chemical kinetics, we typically argue that some of the intermediates are highly reactive, so that they are removed as fast as they are made. We then set the corresponding rates of change to zero. What we are saying is not that these rates are identically zero, of course, but that they are much smaller than the other rates of reaction. The st...

Geometric Singular Perturbation Theory

A new Approach to the Multi-Objective Control of Linear Singular Perturbation Systems

Singular perturbation approach to rattleback reversals

Lagrangian systems with constraints are common models of fundamental or idealized physical systems. Holonomic constraints, typified in the example of a freely moving rigid body, give rise to systems with certain special properties, such as symplectic Hamiltonian systems. Nonholonomic constraints arise in such systems as a disk which rolls without slipping. Holonomic and nonholonomic systems hav...