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Conservation laws and symmetry-driven analysis of a biological population model in porous media.

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Title: Conservation laws and symmetry-driven analysis of a biological population model in porous media.
Authors: Joshi, Urvashi1 (AUTHOR), Sharma, Aniruddha Kumar1 (AUTHOR), Arora, Rajan1 (AUTHOR) rajan.arora@as.iitr.ac.in
Source: Pramana: Journal of Physics. Jun2026, Vol. 100 Issue 2, p1-15. 15p.
Subjects: Population dynamics, Porous materials, Analytical solutions, Population density, Conservation laws (Physics), Symmetry groups, Reaction-diffusion equations
Abstract: This study examines a two-dimensional nonlinear degenerate parabolic partial differential equation (PDE) model that characterises biological population dynamics in porous environments, where fluid flow and nutrient diffusion substantially affect population behaviour. We utilise Lie symmetry analysis to explain the model's intrinsic structure. We establish an optimal system of one-dimensional subalgebras and investigate nonlinear self-adjointness to derive invariant solutions and conservation laws, respectively. We provide new exact solutions that clarify the relationship between population density and the model parameters, including the growth rate (h) and porous constant (θ) . These solutions demonstrate the effect of modifying h and θ on population distribution patterns. Furthermore, conservation laws are derived from the nonlinear self-adjointness property, explaining the conserved quantities of the system. These findings enhance the understanding of population dynamics in porous media and can be applied to predict long-term population behaviour in conditions such as soil and sediments. The study provides a framework for understanding population behaviour under various environmental conditions. [ABSTRACT FROM AUTHOR]
Copyright of Pramana: Journal of Physics is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: Conservation laws and symmetry-driven analysis of a biological population model in porous media.
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  Data: <searchLink fieldCode="AR" term="%22Joshi%2C+Urvashi%22">Joshi, Urvashi</searchLink><relatesTo>1</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Sharma%2C+Aniruddha+Kumar%22">Sharma, Aniruddha Kumar</searchLink><relatesTo>1</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Arora%2C+Rajan%22">Arora, Rajan</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> rajan.arora@as.iitr.ac.in</i>
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  Data: <searchLink fieldCode="JN" term="%22Pramana%3A+Journal+of+Physics%22">Pramana: Journal of Physics</searchLink>. Jun2026, Vol. 100 Issue 2, p1-15. 15p.
– Name: Subject
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  Data: <searchLink fieldCode="DE" term="%22Population+dynamics%22">Population dynamics</searchLink><br /><searchLink fieldCode="DE" term="%22Porous+materials%22">Porous materials</searchLink><br /><searchLink fieldCode="DE" term="%22Analytical+solutions%22">Analytical solutions</searchLink><br /><searchLink fieldCode="DE" term="%22Population+density%22">Population density</searchLink><br /><searchLink fieldCode="DE" term="%22Conservation+laws+%28Physics%29%22">Conservation laws (Physics)</searchLink><br /><searchLink fieldCode="DE" term="%22Symmetry+groups%22">Symmetry groups</searchLink><br /><searchLink fieldCode="DE" term="%22Reaction-diffusion+equations%22">Reaction-diffusion equations</searchLink>
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: This study examines a two-dimensional nonlinear degenerate parabolic partial differential equation (PDE) model that characterises biological population dynamics in porous environments, where fluid flow and nutrient diffusion substantially affect population behaviour. We utilise Lie symmetry analysis to explain the model's intrinsic structure. We establish an optimal system of one-dimensional subalgebras and investigate nonlinear self-adjointness to derive invariant solutions and conservation laws, respectively. We provide new exact solutions that clarify the relationship between population density and the model parameters, including the growth rate (h) and porous constant (θ) . These solutions demonstrate the effect of modifying h and θ on population distribution patterns. Furthermore, conservation laws are derived from the nonlinear self-adjointness property, explaining the conserved quantities of the system. These findings enhance the understanding of population dynamics in porous media and can be applied to predict long-term population behaviour in conditions such as soil and sediments. The study provides a framework for understanding population behaviour under various environmental conditions. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of Pramana: Journal of Physics is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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RecordInfo BibRecord:
  BibEntity:
    Identifiers:
      – Type: doi
        Value: 10.1007/s12043-025-03086-0
    Languages:
      – Code: eng
        Text: English
    PhysicalDescription:
      Pagination:
        PageCount: 15
        StartPage: 1
    Subjects:
      – SubjectFull: Population dynamics
        Type: general
      – SubjectFull: Porous materials
        Type: general
      – SubjectFull: Analytical solutions
        Type: general
      – SubjectFull: Population density
        Type: general
      – SubjectFull: Conservation laws (Physics)
        Type: general
      – SubjectFull: Symmetry groups
        Type: general
      – SubjectFull: Reaction-diffusion equations
        Type: general
    Titles:
      – TitleFull: Conservation laws and symmetry-driven analysis of a biological population model in porous media.
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            NameFull: Joshi, Urvashi
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            NameFull: Sharma, Aniruddha Kumar
      – PersonEntity:
          Name:
            NameFull: Arora, Rajan
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          Dates:
            – D: 01
              M: 06
              Text: Jun2026
              Type: published
              Y: 2026
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              Value: 100
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              Value: 2
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            – TitleFull: Pramana: Journal of Physics
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