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- W1977145800 abstract "On a rectangular parallelopiped in $R^N $, $N geqq 2$, we consider the equation $u_{tt} = Delta u + f(u,u_t )$, where f is a nonlinear perturbation meeting certain conditions. We prove that the above system is locally controllable at $u = 0$, $u_t = 0$; i.e., the set of states in a certain function space which can be reached from $(0,0)$ in a finite time $T < infty $ using boundary controls is an open neighborhood of $(0,0)$ in that function space. These results generalize to the nonlinear case conclusions obtained by Russell for the linear wave equation, in which global controllability was established." @default.
- W1977145800 created "2016-06-24" @default.
- W1977145800 creator A5091660125 @default.
- W1977145800 date "1976-01-01" @default.
- W1977145800 modified "2023-09-26" @default.
- W1977145800 title "Controllability of the Nonlinear Wave Equation in Several Space Variables" @default.
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- W1977145800 doi "https://doi.org/10.1137/0314002" @default.
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