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Discontinuity, Nonlinearity, and Complexity 13(3) (2024) 455--470 | DOI:10.5890/DNC.2024.09.005

Y. Sudha$^1$, V. N. Deiva Mani$^{2,3}$, S. Marshal Anthoni$^2$, K. Murugesan$^1$

$^1$ Department of Mathematics, National Institute of Technology, Tiruchirappalli 620015

$^2$ Department of Mathematics, Anna University Regional Campus, Coimbatore 641046

$^3$ Department of Basic Engineering, Government Polytechnic College, Coimbatore 641014

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Abstract

One of the calamities in the health sector during the recent years is COVID-19(Coronavirus Disease - 2019). The COVID-19 pandemic not only leads to a health crisis but also an economic and social crisis. To retrieve from this situation, it is essential to study the mathematical model of COVID-19. In this paper, a reaction-diffusion COVID-19 model, is considered. The aim of this article is to prove that the considered reaction-diffusion system with variable exponents has a unique weak solution. By regularizing the considered system and by using Faedo-Galerkin method, compactness result, and Gronwall lemma the main objective of the paper is obtained.

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