Global solvability and general decay of a transmission problem for kirchhoff-type wave equations with nonlinear damping and delay term

Zhiqing Liu;  ; Zhong Bo Fang

doi:10.3934/cpaa.2020043

Global solvability and general decay of a transmission problem for kirchhoff-type wave equations with nonlinear damping and delay term

Communications on Pure & Applied Analysis ◽

10.3934/cpaa.2020043 ◽

2020 ◽

Vol 19 (2) ◽

pp. 941-966

Author(s):

Zhiqing Liu ◽

◽

Zhong Bo Fang

Keyword(s):

Wave Equations ◽

Global Solvability ◽

Nonlinear Damping ◽

General Decay ◽

Transmission Problem ◽

Delay Term ◽

Kirchhoff Type ◽

Type Wave

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The global solvability and asymptotic behavior of a transmission problem for Kirchhoff‐type wave equations with memory source on the boundary

Mathematical Methods in the Applied Sciences ◽

10.1002/mma.5722 ◽

2019 ◽

Vol 42 (18) ◽

pp. 6284-6300

Author(s):

Zhiqing Liu ◽

Zhong Bo Fang

Keyword(s):

Asymptotic Behavior ◽

Wave Equations ◽

Global Solvability ◽

Transmission Problem ◽

Kirchhoff Type ◽

Type Wave ◽

Memory Source ◽

With Memory

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General decay of a transmission problem for kirchhoff type wave equations with boundary memory condition

Acta Mathematica Scientia ◽

10.1016/s0252-9602(14)60091-6 ◽

2014 ◽

Vol 34 (5) ◽

pp. 1395-1403 ◽

Cited By ~ 6

Author(s):

Sun Hye PARK

Keyword(s):

Wave Equations ◽

General Decay ◽

Transmission Problem ◽

Memory Condition ◽

Kirchhoff Type ◽

Type Wave

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Stability of a transmission problem for Kirchhoff-type wave equations with memory on the boundary

Mathematical Methods in the Applied Sciences ◽

10.1002/mma.4242 ◽

2016 ◽

Vol 40 (10) ◽

pp. 3528-3537 ◽

Cited By ~ 1

Author(s):

Sun-Hye Park

Keyword(s):

Wave Equations ◽

Transmission Problem ◽

Kirchhoff Type ◽

Type Wave ◽

With Memory

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Existence and asymptotic behaviour of solutions to weakly damped wave equations of Kirchhoff type with nonlinear damping and source terms

Journal of Mathematical Analysis and Applications ◽

10.1016/j.jmaa.2009.07.010 ◽

2010 ◽

Vol 361 (2) ◽

pp. 566-578 ◽

Cited By ~ 15

Author(s):

Takeshi Taniguchi

Keyword(s):

Asymptotic Behaviour ◽

Wave Equations ◽

Nonlinear Damping ◽

Source Terms ◽

Kirchhoff Type ◽

Asymptotic Behaviour Of Solutions ◽

Damping And Source Terms

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Uniform decay for the unilateral problem associated to the Kirchhoff type wave equations with nonlinear boundary damping

Applied Mathematics and Computation ◽

10.1016/j.amc.2003.07.003 ◽

2004 ◽

Vol 156 (1) ◽

pp. 41-57 ◽

Cited By ~ 1

Author(s):

Jeong Ja Bae

Keyword(s):

Wave Equations ◽

Nonlinear Boundary ◽

Uniform Decay ◽

Boundary Damping ◽

Unilateral Problem ◽

Kirchhoff Type ◽

Type Wave

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On transmission problem for kirchhoff type wave equation with a localized nonlinear dissipation in bounded domain

Acta Mathematica Scientia ◽

10.1016/s0252-9602(12)60068-x ◽

2012 ◽

Vol 32 (3) ◽

pp. 893-906 ◽

Cited By ~ 2

Author(s):

Jeong Ja Bae

Keyword(s):

Wave Equation ◽

Bounded Domain ◽

Transmission Problem ◽

Nonlinear Dissipation ◽

Kirchhoff Type ◽

Type Wave

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Blow up and asymptotic behavior for a system of viscoelastic wave equations of Kirchhoff type with a delay term

Advances in the Theory of Nonlinear Analysis and its Application ◽

10.31197/atnaa.389864 ◽

2018 ◽

pp. 146-167

Author(s):

HAKEM ALI ◽

MAHDI FATIMA ZOHRA ◽

FERHAT MOHAMED

Keyword(s):

Asymptotic Behavior ◽

Wave Equations ◽

Blow Up ◽

Delay Term ◽

Kirchhoff Type ◽

Viscoelastic Wave

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Blow up and asymptotic behavior for a system of viscoelastic wave equations of Kirchhoff type with a delay term

Advances in the Theory of Nonlinear Analysis and its Application ◽

10.31197/atnaa.389865 ◽

2018 ◽

Vol 2 (3) ◽

pp. 146-167

Author(s):

Hakem Ali ◽

Mahdi Fatima Zohra ◽

Ferhat Mohamed

Keyword(s):

Asymptotic Behavior ◽

Wave Equations ◽

Blow Up ◽

Delay Term ◽

Kirchhoff Type ◽

Viscoelastic Wave

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General decay rate estimates and numerical analysis for a transmission problem with locally distributed nonlinear damping

Computers & Mathematics with Applications ◽

10.1016/j.camwa.2017.03.012 ◽

2017 ◽

Vol 73 (10) ◽

pp. 2293-2318

Author(s):

Marcelo M. Cavalcanti ◽

Wellington J. Corrêa ◽

Carole Rosier ◽

Flávio R. Dias Silva

Keyword(s):

Numerical Analysis ◽

Decay Rate ◽

Nonlinear Damping ◽

General Decay ◽

Transmission Problem ◽

General Decay Rate

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Degenerate Kirchhoff-type wave problems involving the fractional Laplacian with nonlinear damping and source terms

Journal of Evolution Equations ◽

10.1007/s00028-019-00489-6 ◽

2019 ◽

Vol 19 (3) ◽

pp. 615-643 ◽

Cited By ~ 7

Author(s):

Ning Pan ◽

Patrizia Pucci ◽

Runzhang Xu ◽

Binlin Zhang

Keyword(s):

Fractional Laplacian ◽

Nonlinear Damping ◽

Source Terms ◽

Kirchhoff Type ◽

Type Wave ◽

Damping And Source Terms ◽

Wave Problems

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