Existence Theorems and Galerkin Approximation for Non-Linear Evolution Control Problems

This article presents an optimization problem involving a system governed by a non-linear parabolic equation (dy/dt) + Ay = u where A is a radially continuous, monotone and coercive Volterra operator with the cost functional weakly lower semi-continuous and radially unbounded (coercive). In a first...

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Bibliographic Details
Published inOptimization Vol. 52; no. 3; pp. 287 - 300
Main Author Just, Andrzej
Format Journal Article
LanguageEnglish
Published Taylor & Francis Group 01.06.2003
Subjects
Galerkin Approximation
Mathematics Subject Classification 2000: Primary: 49j20
Non-linear Parabolic Systems
Optimal Control
Secondary: 47h05
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Summary:This article presents an optimization problem involving a system governed by a non-linear parabolic equation (dy/dt) + Ay = u where A is a radially continuous, monotone and coercive Volterra operator with the cost functional weakly lower semi-continuous and radially unbounded (coercive). In a first preparatory part of the article we prove two existence theorems. In the second part we present the Galerkin approximation and we prove existence of the weak and strong condensation points of a set of solution of the approximate optimization problems. Each of this points is a solution of the initial optimization problem. Finally we shall give examples using the obtained results.
ISSN:0233-1934
1029-4945
DOI:10.1080/0233193031000079838