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- W1553604040 abstract "We study the linearised self-excited wave equation x <sub xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>tt</sub> - Δ x-P(x) x <sub xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>t</sub> =0, where P(x)≥0, P(x) L <sup xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>∞</sup> (Ω), in a bounded domain Ω ⊂ R <sup xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>n</sup> with smooth boundary Γ where boundary damping is present. Considering the partition {Γ <sub xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>+</sub> , Γ <sub xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>-</sub> } of the boundary Γ on which x=0 on Γ, and u <sub xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>n</sub> + Ku <sub xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>t</sub> + Lu= 0, on Γ, we find two different bounds for P such that the energy decays exponentially in the energy space as t tends to infinity (Here we assume Γ <sub xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>+</sub> ∩ Γ <sub xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>-</sub> = ø for n > 3). Both bounds depend on Ω (The domain of wave equation in R <sup xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>n</sup> , n ≥ 1). The second bound also depends on the feed-back functions K,L L <sup xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>∞</sup> (Γ <sub xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>+</sub> ) or more precisely depends on a positive function k(x) L <sup xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>∞</sup> (Γ <sub xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>+</sub> ) which determines K and L on the partition Γ <sub xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>+</sub> ." @default.
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- W1553604040 date "1992-06-01" @default.
- W1553604040 modified "2023-09-25" @default.
- W1553604040 title "The Stabilization of a Linearized Self-Excited Wave Equation by an Energy Absorbing Boundary" @default.
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- W1553604040 doi "https://doi.org/10.23919/acc.1992.4792512" @default.
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