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Volume 7, Issue 2
Global Stability of a Parabolic System Involving a Nonlinear Diffusion Operator with an Example in Epidemiology

Achraf Zinihi & Moulay Rchid Sidi Ammi

DOI: 10.12150/jnma.2025.453

J. Nonl. Mod. Anal., 7 (2025), pp. 453-462.

Published online: 2025-04

[An open-access article; the PDF is free to any online user.]

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  • Abstract

The purpose of this work is to study the global stability of specific nonlinear parabolic equations incorporating the $p$-Laplacian operator, with a primary emphasis on their application in biology, particularly in the context of epidemiology. This investigation entails the construction of Lyapunov functions derived from the associated ODEs. To elucidate our approach, we provide an illustrative example from the field of epidemiology.

  • Keywords

Epidemiological model, Lyapunov function, parabolic systems, $p$-Laplacian operator.

  • AMS Subject Headings

92D30, 93D05, 35K40, 35K92

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JNMA-7-453, author = {Zinihi , Achraf and Ammi , Moulay Rchid Sidi}, title = {Global Stability of a Parabolic System Involving a Nonlinear Diffusion Operator with an Example in Epidemiology}, journal = {Journal of Nonlinear Modeling and Analysis}, year = {2025}, volume = {7}, number = {2}, pages = {453--462}, abstract = {

The purpose of this work is to study the global stability of specific nonlinear parabolic equations incorporating the $p$-Laplacian operator, with a primary emphasis on their application in biology, particularly in the context of epidemiology. This investigation entails the construction of Lyapunov functions derived from the associated ODEs. To elucidate our approach, we provide an illustrative example from the field of epidemiology.

}, issn = {2562-2862}, doi = {https://doi.org/10.12150/jnma.2025.453}, url = {http://global-sci.org/intro/article_detail/jnma/23984.html} }
TY - JOUR T1 - Global Stability of a Parabolic System Involving a Nonlinear Diffusion Operator with an Example in Epidemiology AU - Zinihi , Achraf AU - Ammi , Moulay Rchid Sidi JO - Journal of Nonlinear Modeling and Analysis VL - 2 SP - 453 EP - 462 PY - 2025 DA - 2025/04 SN - 7 DO - http://doi.org/10.12150/jnma.2025.453 UR - https://global-sci.org/intro/article_detail/jnma/23984.html KW - Epidemiological model, Lyapunov function, parabolic systems, $p$-Laplacian operator. AB -

The purpose of this work is to study the global stability of specific nonlinear parabolic equations incorporating the $p$-Laplacian operator, with a primary emphasis on their application in biology, particularly in the context of epidemiology. This investigation entails the construction of Lyapunov functions derived from the associated ODEs. To elucidate our approach, we provide an illustrative example from the field of epidemiology.

Zinihi , Achraf and Ammi , Moulay Rchid Sidi. (2025). Global Stability of a Parabolic System Involving a Nonlinear Diffusion Operator with an Example in Epidemiology. Journal of Nonlinear Modeling and Analysis. 7 (2). 453-462. doi:10.12150/jnma.2025.453
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