Exponential Growth of Solutions with $L_{p}$-Norm of a Klein-Gordon Wave Equation with Strong Damping, Source and Delay Terms
DOI:
https://doi.org/10.5890/DNC.2023.06.003Abstract
In this paper we are investigating to figure out the exponential growth of solutions with $L_{p}$-norm of a viscoelastic Klein-Gordon wave equation with strong damping, source and delay terms.References
[1] Berrimi, S. and Messaoudi, S. (2006), Existence and decay of solutions of a viscoelastic equation with a nonlinear source, Nonlinear Analysis: Theory, Methods & Applications, 64(10), 2314-2331.
[2] Kafini, M. and Messaoudi, S. (2020), Local existence and blow up of solutions to a logarithmic nonlinear wave equation with delay, Applicable Analysis, 99(3), 530-547.
[3] Zennir, K. (2013), Exponential growth of solutions with $L_{p}$ -norm of a nonlinear viscoelastic hyperbolic equation, Journal of Nonlinear Sciences & Applications, 6(4), 252-262.
[4] Guo, L., Yuan, Z., and Lin, G. (2015), Blow up and global existence for a nonlinear viscoelastic wave equation with strong damping and nonlinear damping and source terms, Applied Mathematics, 6(5), 806-816.
[5] Agre, K. and Rammaha, M. (2006), Systems of nonlinear wave equations with damping and source terms, Differential and Integral Equations, 19(11), 1235-1270.
[6] Nicaise, S. and Pignotti, C. (2008), Stabilization of the wave equation with boundary or internal distributed delay, Differential and Integral Equations, 21(9-10), 935-958.
[7] Georgiev, V. and Todorova, G. (1994), Existence of solutions of the wave equation with nonlinear damping and source terms, Journal of Differential Equations, 109(2), 295-308.
[8] Wu, S.T. and Tsai, L.Y. (2006), On global existence and blow-up of solutions or an integro-differential equation with strong damping, Taiwanese Journal of Mathematics, 10(4), 979-1014.
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