The hyperbolic singular perturbation problem: An operator theoretic approach
نویسندگان
چکیده
منابع مشابه
A 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 کاملStochastic Economic Growth: An Operator-Theoretic Approach
For many years the trend in macroeconomics has been towards models which are both explicitly stochastic and explicitly dynamic. With these models, researchers seek to replicate and explain observable properties of the major economic time series. One manifestation of this trend towards stochastic dynamic modeling has been increasing use of the inherently dynamic models developed in the field of ...
متن کاملAn operator - theoretic approach to the mixed - sensitivity minimization problem ( I ) by Fabio Fagnani Scuola Normale
in this paper we consider the mixed-sensitivity minimization problem (scalar case).lt gives rise to the so-called two-block problem on the algebra He; we analyze this problem from an operator point of view, using Krein space theory. We obtain a necessary and sufficient condition for the uniqueness of the solution and a parameterization of all solutions in the non-uniqueness case. Moreover, an i...
متن کامل00 4 A singular perturbation problem
Consider the equation −ε 2 ∆u ε + q(x)u ε = f (u ε) in R 3 , |u(∞)| < ∞, ε = const > 0. Under what assumptions on q(x) and f (u) can one prove that the solution u ε exists and lim ε→0 u ε = u(x), where u(x) solves the limiting problem q(x)u = f (u)? These are the questions discussed in the paper.
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: Journal of Differential Equations
سال: 1987
ISSN: 0022-0396
DOI: 10.1016/0022-0396(87)90167-7