Results from a Nonlinear Wave Equation with Acoustic and Fractional Boundary Conditions Coupling by Logarithmic Source and Delay Terms: Global Existence and Asymptotic Behavior of Solutions
Abstract
:1. Introduction
2. Theory and Concepts
- (H1)
- (H2)
- Consequently,
3. Global Existence
4. Decay of Solutions
- where .
- Also, from (41), we find
5. Conclusions
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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Choucha, A.; Boulaaras, S.; Allahem, A.; Alharbi, A.; Jan, R. Results from a Nonlinear Wave Equation with Acoustic and Fractional Boundary Conditions Coupling by Logarithmic Source and Delay Terms: Global Existence and Asymptotic Behavior of Solutions. Mathematics 2024, 12, 2616. https://doi.org/10.3390/math12172616
Choucha A, Boulaaras S, Allahem A, Alharbi A, Jan R. Results from a Nonlinear Wave Equation with Acoustic and Fractional Boundary Conditions Coupling by Logarithmic Source and Delay Terms: Global Existence and Asymptotic Behavior of Solutions. Mathematics. 2024; 12(17):2616. https://doi.org/10.3390/math12172616
Chicago/Turabian StyleChoucha, Abdelbaki, Salah Boulaaras, Ali Allahem, Asma Alharbi, and Rashid Jan. 2024. "Results from a Nonlinear Wave Equation with Acoustic and Fractional Boundary Conditions Coupling by Logarithmic Source and Delay Terms: Global Existence and Asymptotic Behavior of Solutions" Mathematics 12, no. 17: 2616. https://doi.org/10.3390/math12172616
APA StyleChoucha, A., Boulaaras, S., Allahem, A., Alharbi, A., & Jan, R. (2024). Results from a Nonlinear Wave Equation with Acoustic and Fractional Boundary Conditions Coupling by Logarithmic Source and Delay Terms: Global Existence and Asymptotic Behavior of Solutions. Mathematics, 12(17), 2616. https://doi.org/10.3390/math12172616