Exact controllability for multidimensional semilinear hyperbolic equations
Abbreviated Journal Title
SIAM J. Control Optim.
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
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.
Siam Journal on Control and Optimization
"Exact controllability for multidimensional semilinear hyperbolic equations" (2007). Faculty Bibliography 2000s. 7131.