Wave Equation with Acoustic/Memory Boundary Conditions

Vicente, André

doi:10.5269/bspm.v27i1.9066

Cited by 29 publications

(35 citation statements)

References 11 publications

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“…We refer also to [1,11] for some results on the asymptotic stability and global nonexistence results of the wave equation with boundary dissipation of the memory type. A wave equation with acoustic and memory boundary conditions on a part of the boundary of the domain Ω has been also investigated recently in [24], where the existence and uniqueness of global solution have been proved.…”

Section: Introductionmentioning

confidence: 99%

Existence and asymptotic stability of a viscoelastic wave equation with a delay

Kirane

Said‐Houari

2011

Z. Angew. Math. Phys.

143

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In this paper, we consider the viscoelastic wave equation with a delay term in internal feedbacks; namely, we investigate the following problemtogether with initial conditions and boundary conditions of Dirichlet type. Here (x, t) ∈ Ω × (0, ∞), g is a positive real valued decreasing function and μ 1 , μ 2 are positive constants. Under an hypothesis between the weight of the delay term in the feedback and the weight of the term without delay, using the Faedo-Galerkin approximations together with some energy estimates, we prove the global existence of the solutions. Under the same assumptions, general decay results of the energy are established via suitable Lyapunov functionals. Mathematics Subject Classification (2000). 35L05 · 35L15 · 35L70 · 93D15.

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Section: Introductionmentioning

confidence: 99%

Existence and asymptotic stability of a viscoelastic wave equation with a delay

Kirane

Said‐Houari

2011

Z. Angew. Math. Phys.

143

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“…Recently, wave equations with acoustic boundary conditions have been treated by many authors( [11], [13], [5], [1], [6], [10], [12], [3]). In [11], the authors studied the nonlinear wave equations…”

Section: Introductionmentioning

confidence: 99%

Energy Decay Rate for the Kelvin-Voigt Type Wave Equation With Balakrishnan-Taylor Damping and Acoustic Boundary

Kang¹

2016

East Asian mathematical journal

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Abstract. In this paper, we study exponential stabilization of the vibrations of the Kelvin-Voigt type wave equation with Balakrishnan-Taylor damping and acoustic boundary in a bounded domain in R n . To stabilize the systems, we incorporate separately, the internal material damping in the model as like Kang [3]. Energy decay rate are obtained by the exponential stability of solutions by using multiplier technique.

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“…Recently, wave equations with acoustic boundary conditions have been treated by many authors [4], [5], [6], [8], [9], [11], [12], [13]. In [4], the authors studied the nonlinear wave equations…”

Section: Introductionmentioning

confidence: 99%

Energy Decay Rate for the Kirchhoff Type Wave Equation With Acoustic Boundary

Kang¹

2012

East Asian mathematical journal

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Abstract. In this paper, we study uniform exponential stabilization of the vibrations of the Kirchhoff type wave equation with acoustic boundary in a bounded domain in R n . To stabilize the system, we incorporate separately, the passive viscous damping in the model as like Gannesh C. Gorain [1]. Energy decay rate is obtained by the exponential stability of solutions by using multiplier technique.

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Wave Equation with Acoustic/Memory Boundary Conditions

Abstract: In this paper we prove the existence and uniqueness of global solution to the mixed problem for the wave equation with acoustic boundary conditions on a portion of the boundary and memory type conditions on the rest of it.

Cited by 29 publications

References 11 publications

Existence and asymptotic stability of a viscoelastic wave equation with a delay

Existence and asymptotic stability of a viscoelastic wave equation with a delay

Energy Decay Rate for the Kelvin-Voigt Type Wave Equation With Balakrishnan-Taylor Damping and Acoustic Boundary

Energy Decay Rate for the Kirchhoff Type Wave Equation With Acoustic Boundary

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