학술논문
Inverse stability and convergence of difference approximations for boundary value problems for differential inclusions.
Document Type
Journal
Author
Niepage, H.-D. (DDR-HUMB) AMS Author Profile
Source
Subject
34 Ordinary differential equations -- 34A General theory
34A60Differential inclusions
65Numerical analysis -- 65L Ordinary differential equations
65L20Stability and convergence of numerical methods
34A60
65
65L20
Language
English
Abstract
The differential inclusion $Lx\in Fx$, $Bx=b$, is considered, where $L\: H^1\to H^0$ is of first order, $H^1$ and $H^0$ are Sobolev spaces, and $B$ is a bounded linear operator $B\:H^1\to\bold R^n$. A necessary and sufficient condition is given for the stability of the solutions. The condition is used to show discrete weak compactness of a sequence of solutions that are discrete approximations of the solutions to the original inclusion.