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

Öz

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

Anahtar Kelimeler

• Higher-order equation,Growth,, Logarithmic nonlinearity.

Logaritmik Kaynak Terimli Yüksek Mertebeden Viskoelastik Dalga Denkleminin Çözümlerinin Üstel Büyümesi

Öz

Bu çalışma logaritmik kaynak terimli yüksek mertebeden viskoelastik dalga denklemi ile ilgilidir. Uygun koşullar altında çözümlerin üstel büyümesini ispatladık.

Anahtar Kelimeler

• Yüksek mertebeden denklem,Büyüme

Kaynakça

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.