Blow up of Solutions for Viscoelastic Wave Equations of Kirchhoff Type with Variable Exponents
Blow up of Solutions
Keywords:
Blow up, Kirchhoff Type equation, Viscoelastic wave equation, Variable exponent
Abstract
In this work, we consider the blow up of solutions for the viscoelastic wave equation of Kirchhoff type with variable exponents. The present result in this work improve the previous literature.
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References
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S.A. Messaoudi, Blow-up of positive-initial-energy solutions of a nonlinear viscoelastic hyperbolic equation, J. Math. Anal. Appl., 320 (2006) 902-915.
S.A. Messaoudi, A.A. Talahmeh, J.H. Al-Shail, Nonlinear damped wave equation: Existence and blow-up, Comp. Math. Appl., 74 (2017) 3024-3041.
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E. Pişkin, Blow up of solutions for a nonlinear viscoalastic wave equations with variable exponents, Middle East Journal of Science, 5(2) (2019) 134-145.
E. Pişkin and B. Okutmuştur, An Introduction to Sobolev Spaces, Bentham Science, 2021.
M. Ruzicka, Electrorheological Fluids: Modeling and Mathematical Theory, Lecture Notes in Mathematics, Springer, 2000.
H. Song, Blow up arbitrarily positive inital energy solutions for a viscoelastic wave equation, Nonlinear Anal.: Real Worl Appl., 26 (2015) 306-314.
Y. Chen, S. Levine, M. Rao, Variable Exponent, Linear Growth Functionals in Image Restoration, SIAM Journal on Applied Mathematics, 66 (2006) 1383-1406.
L. Diening, P. Hasto, P. Harjulehto, M.M. Ruzicka, Lebesgue and Sobolev Spaces with Variable Exponents, Springer-Verlag, 2011.
X.L. Fan, J.S. Shen, D. Zhao, Sobolev embedding theorems for spaces W^{k,p(x)}(Ω), J. Math. Anal. Appl., 263 (2011) 749-760.
Y. Gao, W. Gao, Existence of weak solutions for viscoelastic hyperbolic equations with variable exponents, Boundary Value Problems, (2013) 1-8.
L. Jie and L. Fei, Blow up of solution for an integro-differential equation with arbitrary positive initial energy, Bondary Value Problems, 96 (2015) 1-10.
O. Kovacik, J. Rakosnik, On spaces L^{p(x)}(Ω), and W^{k,p(x)}(Ω), Czechoslovak Mathematical Journal, 41 (1991) 592-618.
G. Li, L. Hong, W. Liu, Global nonexistence of solutions for viscoelastic wave equations of Kirchhoff type with hifh energy, Journal of Functional Spaces and Applications, (2012) 1-15.
S.A. Messaoudi, Blow up and global existence in a nonlinear viscoelastic wave equation, Math. Nachr., 260 (2003) 58-66.
S.A. Messaoudi, Blow-up of positive-initial-energy solutions of a nonlinear viscoelastic hyperbolic equation, J. Math. Anal. Appl., 320 (2006) 902-915.
S.A. Messaoudi, A.A. Talahmeh, J.H. Al-Shail, Nonlinear damped wave equation: Existence and blow-up, Comp. Math. Appl., 74 (2017) 3024-3041.
S.H. Park, M.J. Lee, J.R. Kang, Blow up results for viscoelastic wave equations with weak damping, Appl. Math. Lett., 80 (2018) 20-26, .
E. Pişkin, Finite time blow up of solutions of the Kirchhoff-type equation with variable exponents, Int. J. Nonlinear Anal. Appl. 11(1) (2020) 37-45.
E. Pişkin, Blow up of solutions for a nonlinear viscoalastic wave equations with variable exponents, Middle East Journal of Science, 5(2) (2019) 134-145.
E. Pişkin and B. Okutmuştur, An Introduction to Sobolev Spaces, Bentham Science, 2021.
M. Ruzicka, Electrorheological Fluids: Modeling and Mathematical Theory, Lecture Notes in Mathematics, Springer, 2000.
H. Song, Blow up arbitrarily positive inital energy solutions for a viscoelastic wave equation, Nonlinear Anal.: Real Worl Appl., 26 (2015) 306-314.
Published
2022-04-14
How to Cite
Pişkin, E., & Butakın, V. (2022). Blow up of Solutions for Viscoelastic Wave Equations of Kirchhoff Type with Variable Exponents. Al-Qadisiyah Journal of Pure Science, 27(1), Math 112-123. https://doi.org/10.29350/qjps.2022.27.2.1480
Issue
Section
Mathematics
Copyright (c) 2022 Erhan Pişkin, Veysel Butakın
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