Global existence and growth of solutions to coupled degeneratly damped Klein-Gordon equations
Keywords:
Klein-Gordon equations, Viscoelastic equations, Degenerate damping
Abstract
We study a system of nonlinear Klein-Gordon equations with viscoelastic and degenerate damping in a bounded domain. We prove the global existence and exponential growth of solutions with negative initial energy.
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References
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[2] F. Yazid, D. Ouchenane, K. Zennir, Global nonexistence of solutions to system of Klein-Gordon equations with degenerate damping and strong source terms in viscoelasticity. Studia Universitatis Babe¸s-Bolyai Mathematica, (2020) 1-17.
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[10] M. A. Rammaha, S. Sakuntasathien, Global existence and blow up of solutions to systems of nonlinear wave equations with degenerate damping and source terms. Nonlinear Analysis: Theory, Methods & Applications, 72 (2010) 2658-2683.
[11] A. Benaissa, D. Ouchenane, K. Zennir, Blow up of positive initial energy solutions to system of nonlinear wave equations with degenerate damping and source terms. Nonlinear Studies, 19(4) (2012) 523-535.
[12] K. Zennir, Growth of solutions to system of nonlinear wave equations with degenerate damping and strong sources. Nonlinear Analysis and Application, 2013 (2013) 1-11.
[13] E. Pi¸skin, Blow up of positive initial-energy solutions for coupled nonlinear wave equations with degenerate damping and source terms. Boundary Value Problems, 43 (2015) 1-11.
[14] ST. Wu, General decay of solutions for a nonlinear sysem of viscoelastic wave equations with degenerate damping and source terms. Journal of Mathematical Analysis and Applications, 406 (2013) 34-48.
[15] K. Zennir, Growth of solutions with positive initial energy to system of degeneratly damped wave equations with memory. Lobachevskii Journal of Mathematics, 35(2) (2014) 147-156.
[16] E. Pi¸skin, F. Ekinci, K. Zennir, Local existence and blow-up of solutions for coupled viscoelastic wave equations with degenerate damping terms. Theoretical and Applied Mechanics, 47(1) (2020) 123-154.
[17] E. Pi¸skin, F. Ekinci, Nonexistence of global solutions for coupled Kirchhoff-type equations with degenerate damping terms. Journal of Nonlinear Functional Analysis 2018 (2018), Article ID 48.
[18] B. Said-Houari, S.A. Messaoudi, A. Guesmia, General decay of solutions of a nonlinear system of viscoelastic wave equations. Nonlinear Di¤erential Equations and Applications NoDEA, 18 (2011) 659-684.
[19] E. Pi¸skin, F. Ekinci, General decay and blow up of solutions for coupled viscoelastic equation of Kirchhoff type with degenerate damping terms. Mathematical Methods in the Applied Sciences, 42(16) (2019) 5468-5488
[2] F. Yazid, D. Ouchenane, K. Zennir, Global nonexistence of solutions to system of Klein-Gordon equations with degenerate damping and strong source terms in viscoelasticity. Studia Universitatis Babe¸s-Bolyai Mathematica, (2020) 1-17.
[3] E. Pi¸skin, Uniform decay and blow-up of solutions for coupled nonlinear Klein-Gordon equations with nonlinear damping terms. Mathematical Methods in the Applied Sciences, 37(18) (2014) 3036-3047.
[4] E. Pi¸skin, Lower bounds for blow-up time of coupled nonlinear Klein-Gordon equations. Gulf Journal of Mathematics, 5(2) (2017) 56-61.
[5] E. Pi¸skin, Blow-up of solutions for coupled nonlinear Klein-Gordon equations with weak damping terms. Mathematical Sciences Letters, 3(3) (2014) 189-191.
[6] Ye Y. Global existence and asymptotic stability for coupled nonlinear Klein–Gordon equations with nonlinear damping terms. Dynamical Systems, 28(2) (2013) 287-298.
[7] M. O. Korpusov, Blow up the solution of a nonlinear system of equations with positive energy. Theoretical and Mathematical Physics, 171(3) (2012) 725-738.
[8] M. M. Miranda, L. A. Medeiros, On the existence of global solutions of a coupled nonlinear Klein-Gordon equations. Funkcialaj Ekvacioj, 30 (1987) 147-161.
[9] S. T. Wu, Blow-up results for system of nonlinear Klein-Gordon equations with arbitrary positive initial energy. Electronic Journal of Differential Equations, 2012 (2012) 1-13.
[10] M. A. Rammaha, S. Sakuntasathien, Global existence and blow up of solutions to systems of nonlinear wave equations with degenerate damping and source terms. Nonlinear Analysis: Theory, Methods & Applications, 72 (2010) 2658-2683.
[11] A. Benaissa, D. Ouchenane, K. Zennir, Blow up of positive initial energy solutions to system of nonlinear wave equations with degenerate damping and source terms. Nonlinear Studies, 19(4) (2012) 523-535.
[12] K. Zennir, Growth of solutions to system of nonlinear wave equations with degenerate damping and strong sources. Nonlinear Analysis and Application, 2013 (2013) 1-11.
[13] E. Pi¸skin, Blow up of positive initial-energy solutions for coupled nonlinear wave equations with degenerate damping and source terms. Boundary Value Problems, 43 (2015) 1-11.
[14] ST. Wu, General decay of solutions for a nonlinear sysem of viscoelastic wave equations with degenerate damping and source terms. Journal of Mathematical Analysis and Applications, 406 (2013) 34-48.
[15] K. Zennir, Growth of solutions with positive initial energy to system of degeneratly damped wave equations with memory. Lobachevskii Journal of Mathematics, 35(2) (2014) 147-156.
[16] E. Pi¸skin, F. Ekinci, K. Zennir, Local existence and blow-up of solutions for coupled viscoelastic wave equations with degenerate damping terms. Theoretical and Applied Mechanics, 47(1) (2020) 123-154.
[17] E. Pi¸skin, F. Ekinci, Nonexistence of global solutions for coupled Kirchhoff-type equations with degenerate damping terms. Journal of Nonlinear Functional Analysis 2018 (2018), Article ID 48.
[18] B. Said-Houari, S.A. Messaoudi, A. Guesmia, General decay of solutions of a nonlinear system of viscoelastic wave equations. Nonlinear Di¤erential Equations and Applications NoDEA, 18 (2011) 659-684.
[19] E. Pi¸skin, F. Ekinci, General decay and blow up of solutions for coupled viscoelastic equation of Kirchhoff type with degenerate damping terms. Mathematical Methods in the Applied Sciences, 42(16) (2019) 5468-5488
Published
2022-01-23
How to Cite
Ekinci, F., & Erhan Pişkin,. (2022). Global existence and growth of solutions to coupled degeneratly damped Klein-Gordon equations. Al-Qadisiyah Journal of Pure Science, 27(1), Math 29-40. https://doi.org/10.29350/qjps.2022.27.1.1461
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Section
Mathematics
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