Exponential growth of solutions of higher-order viscoelastic wave equation with logarithmic term
Yıl 2020,
, 106 - 111, 28.02.2020
Nazlı Irkıl
,
Erhan Pişkin
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.
Kaynakça
- • 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.
Logaritmik Kaynak Terimli Yüksek Mertebeden Viskoelastik Dalga Denkleminin Çözümlerinin Üstel Büyümesi
Yıl 2020,
, 106 - 111, 28.02.2020
Nazlı Irkıl
,
Erhan Pişkin
Öz
Bu çalışma logaritmik kaynak terimli yüksek mertebeden viskoelastik dalga denklemi ile ilgilidir. Uygun koşullar altında çözümlerin üstel büyümesini ispatladık.
Kaynakça
- • 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.