Harnack Estimation for Nonlinear, Weighted, Heat-Type Equation along Geometric Flow and Applications
Abstract
:1. Introduction
2. Preliminaries
3. Harnack Estimation and Applications
1. | 2. |
3. | 4. |
5. | 6. |
7. | 8. |
4. Application to Specific Flows
4.1. Hamilton’s Ricci Flow
4.2. Extended Ricci Flow
5. Conclusions
- (1)
- is a constant function, and , our results reduce to [15],
- (2)
- is a constant function, and , we find the results in [16],
- (3)
- is a constant function, and d is a free variable, then we obtain the results in [20], etc.
Future Aspect
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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Li, Y.; Bhattacharyya, S.; Azami, S.; Saha, A.; Hui, S.K. Harnack Estimation for Nonlinear, Weighted, Heat-Type Equation along Geometric Flow and Applications. Mathematics 2023, 11, 2516. https://doi.org/10.3390/math11112516
Li Y, Bhattacharyya S, Azami S, Saha A, Hui SK. Harnack Estimation for Nonlinear, Weighted, Heat-Type Equation along Geometric Flow and Applications. Mathematics. 2023; 11(11):2516. https://doi.org/10.3390/math11112516
Chicago/Turabian StyleLi, Yanlin, Sujit Bhattacharyya, Shahroud Azami, Apurba Saha, and Shyamal Kumar Hui. 2023. "Harnack Estimation for Nonlinear, Weighted, Heat-Type Equation along Geometric Flow and Applications" Mathematics 11, no. 11: 2516. https://doi.org/10.3390/math11112516