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Approximate Controllability of a Semilinear System Involving a Fully Nonlinear Gradient Term

Approximate Controllability of a Semilinear System Involving a Fully Nonlinear Gradient Term This paper concerns a control system governed by a semilinear degenerate equation involving a fully nonlinear gradient term. The equation may be weakly degenerate and strongly degenerate on a portion of the lateral boundary, and the gradient term can be controlled by the diffusion term. The linearized system is shown to be approximately controllable by constructing a control by means of its conjugate problem. By doing a series of precise compactness estimates, we prove that the semilinear system is approximately controllable. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Applied Mathematics and Optimization Springer Journals

Approximate Controllability of a Semilinear System Involving a Fully Nonlinear Gradient Term

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References (39)

Publisher
Springer Journals
Copyright
Copyright © 2014 by Springer Science+Business Media New York
Subject
Mathematics; Calculus of Variations and Optimal Control; Optimization; Systems Theory, Control; Theoretical, Mathematical and Computational Physics; Mathematical Methods in Physics; Numerical and Computational Physics
ISSN
0095-4616
eISSN
1432-0606
DOI
10.1007/s00245-014-9238-4
Publisher site
See Article on Publisher Site

Abstract

This paper concerns a control system governed by a semilinear degenerate equation involving a fully nonlinear gradient term. The equation may be weakly degenerate and strongly degenerate on a portion of the lateral boundary, and the gradient term can be controlled by the diffusion term. The linearized system is shown to be approximately controllable by constructing a control by means of its conjugate problem. By doing a series of precise compactness estimates, we prove that the semilinear system is approximately controllable.

Journal

Applied Mathematics and OptimizationSpringer Journals

Published: Aug 1, 2014

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