Research Article
Year 2021,
Volume: 70 Issue: 1, 300 - 319, 30.06.2021
Abstract
References
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- 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.
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- Gross, L., Logarithmic sobolev inequalities, American Journal of Mathematics 97 (4) (1975), 1061-1083.
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Existence and decay of solutions for a higher-order viscoelastic wave equation with logarithmic nonlinearity
Abstract
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.
Keywords
References
- 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.
There are 16 citations in total.
Details
| Primary Language | English |
|---|---|
| Subjects | Applied Mathematics |
| Journal Section | Research Article |
| Authors | |
| Submission Date | April 11, 2020 |
| Acceptance Date | January 2, 2021 |
| Publication Date | June 30, 2021 |
| DOI | https://doi.org/10.31801/cfsuasmas.718432 |
| IZ | https://izlik.org/JA37HN32RE |
| Published in Issue | Year 2021 Volume: 70 Issue: 1 |
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Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics
