Araştırma Makalesi
BibTex RIS Kaynak Göster
Yıl 2021, Cilt: 70 Sayı: 1, 300 - 319, 30.06.2021
https://doi.org/10.31801/cfsuasmas.718432

Öz

Kaynakça

  • Adams, R. A. and Fournier, J. J., Sobolev spaces, Elsevier, 2003.
  • 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 99 (1) (2020), 50-74.
  • Al-Gharabli, M. M. and Messaoudi, S. A., The existence and the asymptotic behavior of a plate equation with frictional damping and a logarithmic source term, Journal of Mathematical Analysis and Applications 454 (2) (2017), 1114-1128.
  • Al-Gharabli, M. M. and Messaoudi, S. A., Existence and a general decay result for a plate equation with nonlinear damping and a logarithmic source term, Journal of Evolution Equations 18 (1) (2018), 105-125.
  • Bartkowski, K. and Górka, P., One-dimensional Klein-Gordon equation with logarithmic nonlinearities, Journal of Physics A: Mathematical and Theoretical 41 (35) (2008), 355201.
  • Bialynicki-Birula, I. and Mycielski, J., Wave equations with logarithmic nonlinearities, Bull. Acad. Polon. Sci. Cl 3 (23) (1975), 461.
  • Cazenave, T. and Haraux, A., Équations d'évolution avec non linéarité logarithmique, In Annales de la Faculté des sciences de Toulouse: Mathématiques 2 (1980), 21-51.
  • De Martino, S., Falanga, M., Godano, C. and Lauro, G., Logarithmic Schrödinger-like equation as a model for magma transport, EPL (Europhysics Letters) 63 (3) (2003), 472.
  • Górka, P., Logarithmic Klein-Gordon equation., Acta Physica Polonica B 40 (1) (2009).
  • Gross, L., Logarithmic sobolev inequalities, American Journal of Mathematics 97 (4) (1975), 1061-1083.
  • Han, X., Global existence of weak solutions for a logarithmic wave equation arising from q-ball dynamics, Bull. Korean Math. Soc 50 (1) (2013), 275-283.
  • Martinez, P., A new method to obtain decay rate estimates for dissipative systems, ESAIM: Control, Optimisation and Calculus of Variations 4 (1999), 419-444.
  • Peyravi, A., General stability and exponential growth for a class of semi-linear wave equations with logarithmic source and memory terms, Applied Mathematics & Optimization 81 (2) (2020), 545-561.
  • Piskin, E., Sobolev Spaces, Seçkin Publishing, 2017.
  • Piskin, E. and Irkıl, N., Mathematical behavior of solutions of fourth-order hyperbolic equation with logarithmic source term, In Conference Proceedings of Science and Technology 2 (2019), 27-36.
  • Piskin, E. and Irkıl, N., Well-posedness results for a sixth-order logarithmic boussinesq equation, Filomat 33 (13) (2019), 3985-4000.

Existence and decay of solutions for a higher-order viscoelastic wave equation with logarithmic nonlinearity

Yıl 2021, Cilt: 70 Sayı: 1, 300 - 319, 30.06.2021
https://doi.org/10.31801/cfsuasmas.718432

Öz

The main goal of this paper is to study for the local existence and decay estimates results for a high-order viscoelastic wave equation with logarithmic nonlinerity. We obtain several results: Firstly, by using Feado-Galerkin method and a logaritmic Sobolev inequality, we proved local existence of solutions. Later, we proved general decay results of solutions.

Kaynakça

  • Adams, R. A. and Fournier, J. J., Sobolev spaces, Elsevier, 2003.
  • 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 99 (1) (2020), 50-74.
  • Al-Gharabli, M. M. and Messaoudi, S. A., The existence and the asymptotic behavior of a plate equation with frictional damping and a logarithmic source term, Journal of Mathematical Analysis and Applications 454 (2) (2017), 1114-1128.
  • Al-Gharabli, M. M. and Messaoudi, S. A., Existence and a general decay result for a plate equation with nonlinear damping and a logarithmic source term, Journal of Evolution Equations 18 (1) (2018), 105-125.
  • Bartkowski, K. and Górka, P., One-dimensional Klein-Gordon equation with logarithmic nonlinearities, Journal of Physics A: Mathematical and Theoretical 41 (35) (2008), 355201.
  • Bialynicki-Birula, I. and Mycielski, J., Wave equations with logarithmic nonlinearities, Bull. Acad. Polon. Sci. Cl 3 (23) (1975), 461.
  • Cazenave, T. and Haraux, A., Équations d'évolution avec non linéarité logarithmique, In Annales de la Faculté des sciences de Toulouse: Mathématiques 2 (1980), 21-51.
  • De Martino, S., Falanga, M., Godano, C. and Lauro, G., Logarithmic Schrödinger-like equation as a model for magma transport, EPL (Europhysics Letters) 63 (3) (2003), 472.
  • Górka, P., Logarithmic Klein-Gordon equation., Acta Physica Polonica B 40 (1) (2009).
  • Gross, L., Logarithmic sobolev inequalities, American Journal of Mathematics 97 (4) (1975), 1061-1083.
  • Han, X., Global existence of weak solutions for a logarithmic wave equation arising from q-ball dynamics, Bull. Korean Math. Soc 50 (1) (2013), 275-283.
  • Martinez, P., A new method to obtain decay rate estimates for dissipative systems, ESAIM: Control, Optimisation and Calculus of Variations 4 (1999), 419-444.
  • Peyravi, A., General stability and exponential growth for a class of semi-linear wave equations with logarithmic source and memory terms, Applied Mathematics & Optimization 81 (2) (2020), 545-561.
  • Piskin, E., Sobolev Spaces, Seçkin Publishing, 2017.
  • Piskin, E. and Irkıl, N., Mathematical behavior of solutions of fourth-order hyperbolic equation with logarithmic source term, In Conference Proceedings of Science and Technology 2 (2019), 27-36.
  • Piskin, E. and Irkıl, N., Well-posedness results for a sixth-order logarithmic boussinesq equation, Filomat 33 (13) (2019), 3985-4000.
Toplam 16 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Uygulamalı Matematik
Bölüm Research Article
Yazarlar

Erhan Pişkin 0000-0001-6587-4479

Nazlı Irkıl 0000-0002-9130-2893

Yayımlanma Tarihi 30 Haziran 2021
Gönderilme Tarihi 11 Nisan 2020
Kabul Tarihi 2 Ocak 2021
Yayımlandığı Sayı Yıl 2021 Cilt: 70 Sayı: 1

Kaynak Göster

APA Pişkin, E., & Irkıl, N. (2021). Existence and decay of solutions for a higher-order viscoelastic wave equation with logarithmic nonlinearity. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 70(1), 300-319. https://doi.org/10.31801/cfsuasmas.718432
AMA Pişkin E, Irkıl N. Existence and decay of solutions for a higher-order viscoelastic wave equation with logarithmic nonlinearity. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. Haziran 2021;70(1):300-319. doi:10.31801/cfsuasmas.718432
Chicago Pişkin, Erhan, ve Nazlı Irkıl. “Existence and Decay of Solutions for a Higher-Order Viscoelastic Wave Equation With Logarithmic Nonlinearity”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 70, sy. 1 (Haziran 2021): 300-319. https://doi.org/10.31801/cfsuasmas.718432.
EndNote Pişkin E, Irkıl N (01 Haziran 2021) Existence and decay of solutions for a higher-order viscoelastic wave equation with logarithmic nonlinearity. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 70 1 300–319.
IEEE E. Pişkin ve N. Irkıl, “Existence and decay of solutions for a higher-order viscoelastic wave equation with logarithmic nonlinearity”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., c. 70, sy. 1, ss. 300–319, 2021, doi: 10.31801/cfsuasmas.718432.
ISNAD Pişkin, Erhan - Irkıl, Nazlı. “Existence and Decay of Solutions for a Higher-Order Viscoelastic Wave Equation With Logarithmic Nonlinearity”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 70/1 (Haziran 2021), 300-319. https://doi.org/10.31801/cfsuasmas.718432.
JAMA Pişkin E, Irkıl N. Existence and decay of solutions for a higher-order viscoelastic wave equation with logarithmic nonlinearity. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2021;70:300–319.
MLA Pişkin, Erhan ve Nazlı Irkıl. “Existence and Decay of Solutions for a Higher-Order Viscoelastic Wave Equation With Logarithmic Nonlinearity”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, c. 70, sy. 1, 2021, ss. 300-19, doi:10.31801/cfsuasmas.718432.
Vancouver Pişkin E, Irkıl N. Existence and decay of solutions for a higher-order viscoelastic wave equation with logarithmic nonlinearity. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2021;70(1):300-19.

Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics.

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