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Global exact controllability for quasilinear hyperbolic systems of diagonal form with linearly degenerate characteristics

✍ Scribed by Zhiqiang Wang

Publisher: Elsevier Science
Year: 2008
Tongue: English
Weight: 509 KB
Volume: 69
Category: Article
ISSN: 0362-546X
DOI: 10.1016/j.na.2007.05.037

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✦ Synopsis

This paper deals with the global exact controllability for first-order quasilinear hyperbolic systems of diagonal form with linearly degenerate characteristics. When the system has no zero characteristics, we establish the global exact boundary controllability from one arbitrarily preassigned C 1 data to another by means of a constructive method, in which the desired boundary controls can be acted either on both sides or only on one side. Sharp estimates on the exact controllable time are given in both cases. When the system has some zero characteristics, the global exact controllability is also established.

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## Abstract One often believes that there is no shock formation for the Cauchy problem of quasilinear hyperbolic systems (of conservation laws) with linearly degenerate characteristic fields. It has been a conjecture for a long time (see __Arch. Rational Mech. Anal.__ 2004; **172**:65–91; __Compres