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- W2081416224 abstract "In this paper, solutions of the third-order linear dispersion equations [frac{{partial w}}{{partial t}} + frac{{partial ^3 w}}{{partial x^3 }} = f(x,t)qquad {text{and}}qquad frac{{partial w}}{{partial t}} + frac{{partial ^3 w}}{{partial x^3 }} = 0] are studied for $t geqq 0$, $0 leqq x leqq 2pi $. In the first case, periodic boundary conditions are imposed at 0 and $2pi $ and the distributed control f, which may, however, have support smaller than $[0,2pi ]$, is assumed to be generated by a linear feedback law conserving the “volume” $int_0^{2pi } {w(x,t)dx} $ while monotonically reducing $int_0^{2pi } {w(x,t)^2 dx} $. For the second equation, a feedback boundary control having the same properties is applied. In both cases, uniform exponential decay to a constant state is obtained. Related exact controllability questions are also studied, and affirmative results are obtained." @default.
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- W2081416224 date "1993-05-01" @default.
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- W2081416224 title "Controllability and Stabilizability of the Third-Order Linear Dispersion Equation on a Periodic Domain" @default.
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- W2081416224 doi "https://doi.org/10.1137/0331030" @default.
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