Title

Exact controllability for multidimensional semilinear hyperbolic equations

Authors

Authors

X. Fu; J. Yong;X. Zhang

Comments

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Abbreviated Journal Title

SIAM J. Control Optim.

Keywords

exact controllability; semilinear hyperbolic equation; superlinear; growth; observability inequality; global Carleman estimate; NONLINEAR-WAVE EQUATION; BOUNDARY CONTROLLABILITY; SYSTEMS; DECAY; TIME; Automation & Control Systems; Mathematics, Applied

Abstract

In this paper, we obtain a global exact controllability result for a class of multidimensional semilinear hyperbolic equations with a superlinear nonlinearity and variable coefficients. For this purpose, we establish an observability estimate for the linear hyperbolic equation with an unbounded potential, in which the crucial observability constant is estimated explicitly by a function of the norm of the potential. Such an estimate is obtained by a combination of a pointwise estimate and a global Carleman estimate for the hyperbolic differential operators and analysis on the regularity of the optimal solution to an auxiliary optimal control problem.

Journal Title

Siam Journal on Control and Optimization

Volume

46

Issue/Number

5

Publication Date

1-1-2007

Document Type

Article

Language

English

First Page

1578

Last Page

1614

WOS Identifier

WOS:000251836900003

ISSN

0363-0129

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