Persistent regional null controllability of some degenerate wave equations |
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| Authors: | Muming Zhang Hang Gao |
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| Affiliation: | School of Mathematics and Statistics, Northeast Normal University, Changchun, China |
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| Abstract: | This paper is addressed to a study of the persistent regional null controllability problems for one‐dimensional linear degenerate wave equations through a distributed controller. Different from non‐degenerate wave equations, the classical null controllability results do not hold for some degenerate wave equations. Thus, persistent regional null controllability is introduced, which means finding a control such that the corresponding state of the degenerate wave equation may vanish in a suitable subset of the space domain in a period of time. In order to solve this problem, we need to establish the regional null controllability for degenerate wave equations. This problem is reduced to a suitable observability problem of a linear degenerate wave equation. The key point is to choose a suitable multiplier in order to establish this observability inequality. Copyright © 2017 John Wiley & Sons, Ltd. |
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| Keywords: | persistent regional null controllability observability degenerate wave equation |
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