Lie Symmetries of Nonlinear Parabolic-Elliptic Systems and Their Application to a Tumour Growth Model
Abstract
:1. Introduction
2. Form-Preserving Transformations for the Class of Systems (3)
3. Lie Symmetries of a Class of Parabolic-Elliptic Systems
4. Boundary Value Problems for a One-Dimensional Tumour Growth Model with Negligible Cell Viscosity
5. Higher-Dimensional Tumour Growth Model without Cell Viscosity
6. Conclusions
Author Contributions
Acknowledgments
Conflicts of Interest
References
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Case | RD System | Basic Operators of MAI |
---|---|---|
1. | ||
2. | ||
3. | ||
4. | ||
5. | ||
6. | ||
7. | ||
8. | ||
9. | ||
10. | ||
11. | ||
12. | ||
13. | ||
14. | ||
Case | RD System | Basic Operators of MAI |
---|---|---|
1. | ||
2. | ||
3. | ||
4. | ||
5. | ||
6. | ||
7. | ||
8. | ||
9. | ||
10. | ||
11. | ||
12. | ||
13. | ||
14. | ||
15. | ||
16. | ||
17. | ||
18. | ||
19. | ||
20. | ||
21. | ||
RD System | Transformation of Variables | Case of Table 1 | |
---|---|---|---|
1. | 3 | ||
with | |||
2. | 4 | ||
with | |||
3. | 8 | ||
4. | 8 | ||
5. | 9 | ||
6. | 9 | ||
7. | 10 | ||
with | |||
8. | 11 | ||
with |
RD System | Transformation of Variables | Case of Table 2 | |
---|---|---|---|
1. | 6 | ||
2. | 7 | ||
3. | 9, if | ||
11, if | |||
4. | 10 | ||
5. | 11 | ||
6. | 12 | ||
7. | 12 | ||
8. | 13 | ||
9. | 13 | ||
10. | 16 | ||
11. | 17 | ||
12. | 19, if | ||
21, if | |||
13. | 20 | ||
14. | 21 | ||
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Cherniha, R.; Davydovych, V.; King, J.R. Lie Symmetries of Nonlinear Parabolic-Elliptic Systems and Their Application to a Tumour Growth Model. Symmetry 2018, 10, 171. https://doi.org/10.3390/sym10050171
Cherniha R, Davydovych V, King JR. Lie Symmetries of Nonlinear Parabolic-Elliptic Systems and Their Application to a Tumour Growth Model. Symmetry. 2018; 10(5):171. https://doi.org/10.3390/sym10050171
Chicago/Turabian StyleCherniha, Roman, Vasyl’ Davydovych, and John R. King. 2018. "Lie Symmetries of Nonlinear Parabolic-Elliptic Systems and Their Application to a Tumour Growth Model" Symmetry 10, no. 5: 171. https://doi.org/10.3390/sym10050171