| Citation: |
Jing Zhang, Zenggui Wang. LIE SYMMETRY AND EXACT SOLUTIONS FOR THE POROUS MEDIUM EQUATION[J]. Journal of Applied Analysis & Computation, 2025, 15(2): 934-950. doi: 10.11948/20240212
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LIE SYMMETRY AND EXACT SOLUTIONS FOR THE POROUS MEDIUM EQUATION
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Abstract
This paper aims to study a (2+1)-dimensional Biological population model with the porous medium by Lie symmetry method. By using commutation tables, the one-dimensional optimal subalgebras for the porous medium equation is given. Group invariant solutions of this model are constructed by the reduction equations. Further, the dynamic behavior of the model graphically is presented.
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Keywords:
- Porous medium equation /
- Lie symmetry method /
- optimal system /
- exact solutions
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References
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Jing Zhang, Zenggui Wang. LIE SYMMETRY AND EXACT SOLUTIONS FOR THE POROUS MEDIUM EQUATION[J]. Journal of Applied Analysis & Computation, 2025, 15(2): 934-950. doi: 10.11948/20240212
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Figure 1.
The solution (3.24) at
$ c_{1}=1,c_{2}=10 $ $ y $ $ t=5 $ $ t=7 $ $ t=8 $ -
Figure 2.
The solution (3.28) at
$ c_{1}=2,c_{2}=3 $ $ t=1 $ $ t $ $ x = 5, x = 10, x = 20 $ $ y = 0 $ $ x $ $ t=5 $ $ t=7 $ $ t=8 $ $ y=1 $