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arXiv · 1509.00545

Null controllability of some degenerate wave equations

Muming Zhang·Hang Gao
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Abstract

This paper is devoted to a study of the null controllability problems for one-dimensional linear degenerate wave equations through a boundary controller. First, the well-posedness of linear degenerate wave equations is discussed. Then the null controllability of some degenerate wave equations is established, when a control acts on the non-degenerate boundary. Different from the known controllability results in the case that a control acts on the degenerate boundary, any initial value in state space is controllable in this case. Also, an explicit expression for the controllability time is given. Furthermore, a counterexample on the controllability is given for some other degenerate wave equations.

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Muming Zhang, Hang Gao. 2015-11-20. Null controllability of some degenerate wave equations. https://arxiv.org/abs/1509.00545

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