Oscillatory boundary conditions for acoustic wave equations

Gal, Ciprian G.; Goldstein, Gisèle Ruiz; Goldstein, Jerome A.

doi:10.1007/978-3-0348-7924-8_32

Cited by 38 publications

(55 citation statements)

References 5 publications

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“…More recently the interest for acoustic boundary condition has revived. See, for example, [7,8,14,15,26,31].…”

Section: Introductionmentioning

confidence: 99%

Attractors for semilinear damped wave equations with an acoustic boundary condition

Frigeri

2009

J. Evol. Equ.

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In this paper, we study a semilinear weakly damped wave equation equipped with an acoustic boundary condition. The problem can be considered as a system consisting of the wave equation describing the evolution of an unknown function u = u(x, t), x ∈ in the domain coupled with an ordinary differential equation for an unknown function δ = δ(x, t), x ∈ := ∂ on the boundary. A compatibility condition is also added due to physical reasons. This problem is inspired on a model originally proposed by Beale and Rosencrans (Bull Am Math Soc 80:1276-1278, 1974. The goal of the paper is to analyze the global asymptotic behavior of the solutions. We prove the existence of an absorbing set and of the global attractor in the energy phase space. Furthermore, the regularity properties of the global attractor are investigated. This is a difficult issue since standard techniques based on the use of fractional operators cannot be exploited. We finally prove the existence of an exponential attractor. The analysis is carried out in dependence of two damping coefficients.

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“…More recently the interest for acoustic boundary condition has revived. See, for example, [7,8,14,15,26,31].…”

Section: Introductionmentioning

confidence: 99%

Attractors for semilinear damped wave equations with an acoustic boundary condition

Frigeri

2009

J. Evol. Equ.

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“…For the moment assume θ = 0 (no damping and that the coupling is linear, i.e., η(s) = s. This reduces (1)-(6) to a model which has already been considered in many references [5][6][7][8][9][10][11]13,19]. From a linear semigroup point of view, the interesting feature of this problem is that the resolvent is not compact [5], and therefore approaches to studying stability based on Nagy-Foias theory or the LaSalle Invariance Principle are inapplicable.…”

Section: Description Of the Problemmentioning

confidence: 99%

“…In such a case, there is no reason to include the presence of a nonlinear damping force. On the other hand, if the structure has non-negligible mass (i.e., m > 0), then in general solutions are unstable [5,11]. See also [1], which studies a similar boundary condition and shows that the presence of the z tt term in the dynamics causes the solutions to be unstable.…”

Section: Description Of the Problemmentioning

confidence: 99%

“…From a physical point of view, however, it is more realistic to assume positive mass, as all real-world structures possess some mass. In the linear model, there is a disparity between theoretical results showing stability [10,13,19] for m ≡ 0 and those proving lack of stability [5,11] for m > 0. To resolve this disparity, in Sect.…”

Section: Description Of the Problemmentioning

confidence: 99%

“…Multiply (1) by φ ∈ H 1 0 ( ) and (3) by ψ ∈ L 2 ( 1 ) and integrate by parts (Green's formula) to obtain (10) and (11). Most of the desired regularity properties are clear; it remains merely to show that u t , θ(u t ) ∈ L 2 ( 1 ) (where 1 …”

Section: Existence Of Weak Solutionsmentioning

confidence: 99%

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Uniform boundary stabilization of a wave equation with nonlinear acoustic boundary conditions and nonlinear boundary damping

Graber

2011

J. Evol. Equ.

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International audienceWe consider a wave equation with nonlinear acoustic boundary conditions. This is a nonlinearly coupled system of hyperbolic equations modeling an acoustic/structure interaction, with an additional boundary damping term to induce both existence of solutions as well as stability. Using the methods of Lasiecka and Tataru for a wave equation with nonlinear boundary damping, we demonstrate well-posedness and uniform decay rates for solutions in the finite energy space, with the results depending on the relationship between (i) the mass of the structure, (ii) the nonlinear coupling term, and (iii) the size of the nonlinear damping. We also show that solutions (in the linear case) depend continuously on the mass of the structure as it tends to zero, which provides rigorous justification for studying the case where the mass is equal to zero

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Graphene‐based dual‐function acoustic transducers for machine learning‐assisted human–robot interfaces

Sun

Gao

Guo

et al. 2022

InfoMat

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Human-robot interface (HRI) electronics are critical for realizing robotic intelligence. Here, we report graphene-based dual-function acoustic transducers for machine learning-assisted human-robot interfaces (GHRI). The GHRI functions both an artificial ear through the triboelectric acoustic sensing mechanism and an artificial mouth through the thermoacoustic sound emission mechanism. The success of the integrated device is also attributed to the multifunctional laser-induced graphene, as either triboelectric materials, electrodes, or thermoacoustic sources. By systematically optimizing the structure parameters, the GHRI achieves high sensitivity (4500 mV Pa -1 ) and operating durability (1 000 000 cycles and 60 days), capable of recognizing speech identities, emotions, content, and other information in the human speech. With the assistance of machine learning, 30 speech categories are trained by a convolutional neural network, and the accuracy reaches 99.66% and 96.63% in training datasets and test datasets. Furthermore, GHRI is used for artificial intelligence communication based on recognized speech features. Our work shows broad prospects for the development of robotic intelligence.

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Oscillatory boundary conditions for acoustic wave equations

Cited by 38 publications

References 5 publications

Attractors for semilinear damped wave equations with an acoustic boundary condition

Attractors for semilinear damped wave equations with an acoustic boundary condition

Uniform boundary stabilization of a wave equation with nonlinear acoustic boundary conditions and nonlinear boundary damping

Graphene‐based dual‐function acoustic transducers for machine learning‐assisted human–robot interfaces

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