QUALITATIVE ANALYSIS OF A WAVE EQUATION WITH BALAKRISHNAN-TAYLOR DAMPING AND LOGARITHMIC SOURCE TERMS

N. Boumaza; B. Gheraibia; G. Liu; M. Shahrouzi; Kh. Zennir

doi:10.11948/20250330

2027 Volume 17 Issue 1

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N. Boumaza, B. Gheraibia, G. Liu, M. Shahrouzi, Kh. Zennir. QUALITATIVE ANALYSIS OF A WAVE EQUATION WITH BALAKRISHNAN-TAYLOR DAMPING AND LOGARITHMIC SOURCE TERMS[J]. Journal of Applied Analysis & Computation, 2027, 17(1): 255-268. doi: 10.11948/20250330

Citation:

N. Boumaza, B. Gheraibia, G. Liu, M. Shahrouzi, Kh. Zennir. QUALITATIVE ANALYSIS OF A WAVE EQUATION WITH BALAKRISHNAN-TAYLOR DAMPING AND LOGARITHMIC SOURCE TERMS[J]. Journal of Applied Analysis & Computation, 2027, 17(1): 255-268. doi: 10.11948/20250330

QUALITATIVE ANALYSIS OF A WAVE EQUATION WITH BALAKRISHNAN-TAYLOR DAMPING AND LOGARITHMIC SOURCE TERMS

1.
Department of Mathematics, Laboratory of Mathematics, Informatics and System (LAMIS), Echahid Cheikh Larbi Tebessi University, Tebessa, Algeria
2.
Department of Mathematics and Computer Science, Larbi Ben M'Hidi University, Oum El-Bouaghi, Algeria
3.
School of Mathematics and Statistics, Henan University of Technology, Zhengzhou 450001, China
4.
Department of Applied Mathematics, Faculty of Mathematical Sciences, Ferdowsi University of Mashhad, P.O.Box 1159, Mashhad 91775, Iran
5.
Department of Mathematics, College of Science, Qassim University, Saudi Arabia

Author Bio: Email: nouri.boumaza@univ-tebessa.dz(A. Boumaaza); Email: billel.gheraibia@univ-oeb.dz(B. Gheraibia); Email: shahrouzi@um.ac.ir(M. Shahrouzi); Email: k.zennir@qu.edu.sa(Kh. Zennir)
Corresponding author: Email: gongweiliu@haut.edu.cn(G. Liu)
Fund Project: The authors are grateful the referees for their careful reading of this paper and the valuable comments to improve the presentation of the paper. The project is supported by Natural Science Foundation of Henan Province (No. 252300421984)

Abstract

Abstract

The main objective of this work is to investigate an initial–boundary value problem for a wave equation incorporating Balakrishnan–Taylor damping, weak damping, and a logarithmic source term. By employing the potential well method combined with an appropriate logarithmic Sobolev inequality, we establish the global existence and energy decay of solutions in the stable set of initial data. In addition, we show that when the initial data lie in the unstable set, the corresponding solutions blow up in infinite time in the cases $ E(0)<d $ and $ E(0)<0 $. These results provide a comprehensive description of the long-term behavior of solutions, highlighting the balance between dissipative effects and the logarithmic nonlinearity.
- Wave equation /
- Balakrishnan-Taylor damping /
- logarithmic nonlinearity /
- global existence /
- general decay /
- blow up /
- nonlinear equations
MSC: 35B15, 26A33

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