Invariance Analysis, Symmetry Reduction and Conservation Laws for Biological Population in Porous Media
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866909419070029824 |
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| author | Joshi, Urvashi Sharma, Aniruddha Kumar Arora, Rajan |
| author_facet | Joshi, Urvashi Sharma, Aniruddha Kumar Arora, Rajan |
| contents | This research paper talks about using complex mathematical tools to study and figure out the behavior of biological populations in porous media. Porous media offer a unique environment where various factors, including fluid flow and nutrient diffusion, significantly influence population dynamics. The theory of Lie symmetries is used to find inherent symmetries in the governing equation of the population model, helping to find conservation laws and invariant solutions. The derivation and analysis of the optimal system provide insights into the most influential parameters affecting population growth and distribution. Furthermore, the study explores the construction of invariant solutions, which aid in characterizing long-term population behavior. The article concludes with the non-linear self-adjointness property and conservation laws for the model. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_05314 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Invariance Analysis, Symmetry Reduction and Conservation Laws for Biological Population in Porous Media Joshi, Urvashi Sharma, Aniruddha Kumar Arora, Rajan Analysis of PDEs This research paper talks about using complex mathematical tools to study and figure out the behavior of biological populations in porous media. Porous media offer a unique environment where various factors, including fluid flow and nutrient diffusion, significantly influence population dynamics. The theory of Lie symmetries is used to find inherent symmetries in the governing equation of the population model, helping to find conservation laws and invariant solutions. The derivation and analysis of the optimal system provide insights into the most influential parameters affecting population growth and distribution. Furthermore, the study explores the construction of invariant solutions, which aid in characterizing long-term population behavior. The article concludes with the non-linear self-adjointness property and conservation laws for the model. |
| title | Invariance Analysis, Symmetry Reduction and Conservation Laws for Biological Population in Porous Media |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2412.05314 |