Spectral deformation in a problem of singular perturbation theory
نویسندگان
چکیده
منابع مشابه
INVESTIGATION OF BOUNDARY LAYERS IN A SINGULAR PERTURBATION PROBLEM INCLUDING A 4TH ORDER ORDINARY DIFFERENTIAL EQUATIONS
In this paper, we investigate a singular perturbation problem including a fourth order O.D.E. with general linear boundary conditions. Firstly, we obtain the necessary conditions of solution of O.D.E. by making use of fundamental solution, then by compatibility of these conditions with boundary conditions, we determine that, for given perturbation problem, whether boundary layer is formed or not.
متن کاملFirst order spectral perturbation theory of square singular matrix pencils
Let H(λ) = A0 + λA1 be a square singular matrix pencil, and let λ0 ∈ C be an eventually multiple eigenvalue of H(λ). It is known that arbitrarily small perturbations of H(λ) can move the eigenvalues of H(λ) anywhere in the complex plane, i.e., the eigenvalues are discontinuous functions of the entries of A0 and A1. Therefore, it is not possible to develop an eigenvalue perturbation theory for a...
متن کاملA Schrödinger singular perturbation problem
Consider the equation −ε∆uε + q(x)uε = f(uε) in R3, |u(∞)| < ∞, ε = const > 0. Under what assumptions on q(x) and f(u) can one prove that the solution uε exists and limε→0 uε = u(x), where u(x) solves the limiting problem q(x)u = f(u)? These are the questions discussed in the paper.
متن کاملA 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 ...
متن کاملSingular 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...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Доклады Академии наук
سال: 2019
ISSN: 0869-5652
DOI: 10.31857/s0869-56524844397-400