منابع مشابه
Singular perturbation problems for nonlinear elliptic equations in degenerate settings
Here N ≥ 1, g(s) ∈ C(R,R) is a function with a subcritical growth, V (x) ∈ C(R ,R) is a positive function and 0 < ε 1. Among solutions of (0.1)ε, we are interested in concentrating families (uε) of solutions, which have the following behavior: (i) uε(x) has a local maximum at xε ∈ R and xε converges to some x0 ∈ R as ε → 0. (ii) rescaled function vε(y) = uε(εy + xε) converges as ε → 0 to a solu...
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 ...
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We investigate the asymptotic behavior of some anisotropic diffusion problems and give some estimates on the rate of convergence of the solution toward its limit. We also relate this type of elliptic problems to problems set in cylinder becoming unbounded in some directions and show how some information on one type leads to information for the other type and conversely. 1. A model problem The g...
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The present paper deals with a survey of numerical techniques for solving nonlinear elliptic singular perturbation problems, developed by numerous researchers in a chronological order as the field developed year after year from 1985. A large amount of research material related to nonlinear elliptic singularly perturbed problems has been collected with the aim of introduction to some of the idea...
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Sufficient conditions for the existence and uniqueness, and estimates, of a continuous vector solution y = y(t) to the integral equation y(t) = u(t) + EL(t) Ef t M(s) f(s,y(s)) ds + K(t,s) f(s,y(s)) ds, t 0 are derived. A successive approximation technique involving a double sequence is used in the proof . This integral equation result is applied to the second order singular perturbation proble...
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ژورنال
عنوان ژورنال: Bulletin of the Australian Mathematical Society
سال: 1977
ISSN: 0004-9727,1755-1633
DOI: 10.1017/s0004972700025582