Research Article

Exponential growth of solutions of higher-order viscoelastic wave equation with logarithmic term

Volume: 13 Number: ÖZEL SAYI I February 28, 2020
EN TR

Exponential growth of solutions of higher-order viscoelastic wave equation with logarithmic term

Abstract

This paper deals with a higher-order viscoelastic wave equation with logarithmic source term. We prove, for suitable conditions, the exponential growth of solutions.

Keywords

References

  1. • Al-Gharabli, M.M., Guesmia A. and Messaoudi, S.A., Well posedness and asymptotic stability results for a viscoelastic plate equation with a logarithmic nonlinearity, Applicable Analysis, 1-18.• Al-Gharabli, M.M., Guesmia A. and Messaoudi, S.A., (2019), Existence and a general decay results for a viscoelastic plate equation with a logarithmic nonlinearity, 159-180.• Bartkowski, K. and Gorka, P., (2008), One-dimensional Klein--Gordon equation with logarithmic nonlinearities, J. Phys. A., 41(35) 1-11.• Bialynicki-Birula, I. and Mycielski, J., (1975), Wave equations with logarithmic nonlinearities, Bull. Acad. Polon. Sci. Ser. Sci. Math. Astron. Phys., 23(4) 461-466.• Buljan, H., Siber,,A, Soljacic, M., Schwartz, T., M.,Segev, D. N., Christodoulides, (2003), Incoherent white light solitons in logarithmically saturable noninstantaneous nonlinear media, Phys. Rev., E (3) 68.• Cavalcanti, M., Cavalcanti, V.N.D. and Soriano, J.A., (2002), Exponential decay for the solution of semi linear viscoelastic wave equations with localized damping, Electron. J. Differ. Equ. 2002, 1-14.• Cazenave, T. and Haraux, A.,(1980), Equations d'evolution avec non linéarité logarithmique, Ann. Fac. Sci. Toulouse 2(1), 21-51.• Dafermos, C., (1970), Asypmtotic stability in viscoelasticity, Arch. Ration. Mech. Anal., 37, 297-308.• Martino, D., Falanga, M., Godano,C. and Lauro, G., (2003), Logarithmic Schrödinger-like equation as a model for magma transport, Europhys. Lett., 63(3), 472-475.• Gorka, P., (2009), Logarithmic Klein--Gordon equation, Acta Phys. Pol. B 40(1), 59-66.• Gross, L., (1975), Logarithmic Sobolev inequalities, Amer. J. Math. 97(4),1061-1083.• Han, X.S., (2013), Global existence of weak solutions for a logarithmic wave equation arising from Q-ball dynamics, Bull. Korean Math. Soc. 50(1), 275--283.• Messaoudi, S.A. and Al-Gharabli, (2017), Existence and a general decay result for a plate equation with nonlinear damping and a logarithmic source term, Journal of Evolution Equations, 18(1),105-125.• Messaoudi, S.A. and Al-Gharabli, (2017), The existence and the asymptotic behavior of a plate equation with frictional damping and a logarithmic source term, J. Math. Anal. Appl., 454, 1114-1128.• Peyravi, A., (2018), General stability and exponential growth for a class of semi-linear wave equations with logarithmic source and memory terms., Appl. Math. Optim.,1-17.

Details

Primary Language

English

Subjects

Engineering

Journal Section

Research Article

Publication Date

February 28, 2020

Submission Date

October 24, 2019

Acceptance Date

February 21, 2020

Published in Issue

Year 2020 Volume: 13 Number: ÖZEL SAYI I

APA
Irkıl, N., & Pişkin, E. (2020). Exponential growth of solutions of higher-order viscoelastic wave equation with logarithmic term. Erzincan University Journal of Science and Technology, 13(ÖZEL SAYI I), 106-111. https://doi.org/10.18185/erzifbed.637784
AMA
1.Irkıl N, Pişkin E. Exponential growth of solutions of higher-order viscoelastic wave equation with logarithmic term. Erzincan University Journal of Science and Technology. 2020;13(ÖZEL SAYI I):106-111. doi:10.18185/erzifbed.637784
Chicago
Irkıl, Nazlı, and Erhan Pişkin. 2020. “Exponential Growth of Solutions of Higher-Order Viscoelastic Wave Equation With Logarithmic Term”. Erzincan University Journal of Science and Technology 13 (ÖZEL SAYI I): 106-11. https://doi.org/10.18185/erzifbed.637784.
EndNote
Irkıl N, Pişkin E (February 1, 2020) Exponential growth of solutions of higher-order viscoelastic wave equation with logarithmic term. Erzincan University Journal of Science and Technology 13 ÖZEL SAYI I 106–111.
IEEE
[1]N. Irkıl and E. Pişkin, “Exponential growth of solutions of higher-order viscoelastic wave equation with logarithmic term”, Erzincan University Journal of Science and Technology, vol. 13, no. ÖZEL SAYI I, pp. 106–111, Feb. 2020, doi: 10.18185/erzifbed.637784.
ISNAD
Irkıl, Nazlı - Pişkin, Erhan. “Exponential Growth of Solutions of Higher-Order Viscoelastic Wave Equation With Logarithmic Term”. Erzincan University Journal of Science and Technology 13/ÖZEL SAYI I (February 1, 2020): 106-111. https://doi.org/10.18185/erzifbed.637784.
JAMA
1.Irkıl N, Pişkin E. Exponential growth of solutions of higher-order viscoelastic wave equation with logarithmic term. Erzincan University Journal of Science and Technology. 2020;13:106–111.
MLA
Irkıl, Nazlı, and Erhan Pişkin. “Exponential Growth of Solutions of Higher-Order Viscoelastic Wave Equation With Logarithmic Term”. Erzincan University Journal of Science and Technology, vol. 13, no. ÖZEL SAYI I, Feb. 2020, pp. 106-11, doi:10.18185/erzifbed.637784.
Vancouver
1.Nazlı Irkıl, Erhan Pişkin. Exponential growth of solutions of higher-order viscoelastic wave equation with logarithmic term. Erzincan University Journal of Science and Technology. 2020 Feb. 1;13(ÖZEL SAYI I):106-11. doi:10.18185/erzifbed.637784

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