Local and Global Existence of Solution for Love Type Waves with Past History
Abstract
:1. Introduction
2. Existence and Uniqueness of Local Weak Solution
3. Global Solution
4. Conclusions
- We proved our results without need of how to decrease for the kernel function.
- In our previous work, we restricted on the case where , which is not the case in these studies.
- There are several generalizations and contributions that are very important in terms of the system itself. We proposed a damped system related to a large number (infinite) of sources, each one has functionality and physical properties, and we look at the overlapping of these terms. Which makes the problem have very wide applications and important in terms of applications in modern science, especially when it comes in bounded domain.
- Quantitatively, we used and developed the stable set method named potential well method, with details to study the global existence of solution commensurate with the bounded domain after proving the local existence of solution using a usual method, Faedo–Galerkin method.
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
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Biomy, M.; Zennir, K.; Himadan, A. Local and Global Existence of Solution for Love Type Waves with Past History. Mathematics 2020, 8, 1998. https://doi.org/10.3390/math8111998
Biomy M, Zennir K, Himadan A. Local and Global Existence of Solution for Love Type Waves with Past History. Mathematics. 2020; 8(11):1998. https://doi.org/10.3390/math8111998
Chicago/Turabian StyleBiomy, Mohamed, Khaled Zennir, and Ahmed Himadan. 2020. "Local and Global Existence of Solution for Love Type Waves with Past History" Mathematics 8, no. 11: 1998. https://doi.org/10.3390/math8111998
APA StyleBiomy, M., Zennir, K., & Himadan, A. (2020). Local and Global Existence of Solution for Love Type Waves with Past History. Mathematics, 8(11), 1998. https://doi.org/10.3390/math8111998