Exact controllability for first order quasilinearhyperbolic systems with internal controls

Kaili  Zhuang; Tatsien Li; Bopeng  Rao

doi:10.3934/dcds.2016.36.1105

Article Contents

2016, Volume 36, Issue 2: 1105-1124. Doi: 10.3934/dcds.2016.36.1105

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Exact controllability for first order quasilinear hyperbolic systems with internal controls

1.
School of Mathematical Sciences, Fudan University, Shanghai 200433

Received: May 2014

Published: May 2017

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Abstract

Based on the theory of the local exact boundary controllability for first order quasilinear hyperbolic systems, using an extension method, the authors establish the exact controllability in a shorter time by means of internal controls acting on suitable domains. In particular, under certain special but reasonable hypotheses, the exact controllability can be realized only by internal controls, and the control time can be arbitrarily small.

Keywords:

First order quasilinear hyperbolic system,
$C^1$ classical solution,
local exact controllability,
boundary control,
internal control.

Mathematics Subject Classification: Primary: 35L04, 49J20; Secondary: 93B05.

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References

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