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All Journal Limits: Journal of Mathematics and Its Applications
Trynita, Annisa Diva Putri
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Computer Science & IT Mathematics

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Diffusion-Advection Reaction in Gierer-Meindhart System Trynita, Annisa Diva Putri; Sutrima, Sutrima
Limits: Journal of Mathematics and Its Applications Vol. 22 No. 2 (2025): Limits: Journal of Mathematics and Its Applications Volume 22 Nomor 2 Edisi Ju
Publisher : Pusat Publikasi Ilmiah LPPM Institut Teknologi Sepuluh Nopember

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.12962/limits.v22i2.3471

Abstract

Gierer-Meinhardt system is a mathematical model commonly used to describe chemical and biological phenomena, specifically the interaction between two types of molecules: activator and inhibitor. Diffusion reactions are processes where chemical molecules move from areas of high concentration to areas of low concentration randomly. In this research, the Gierer Meinhardt system with advection components is considered. The mathematical model developed consists of partial differential equations (PDE) for two variables, namely the activator and the inhibitor, with the addition of an advection component that depends on the flow speed. Studies show that the presence of advection significantly affects the characteristics of the patterns formed. Advection reactions cause more regular and oriented patterns compared to patterns produced only by diffusion. This research uses theoretical analysis methods and literature studies to analyze the impact of advection-diffusion reactions on the Gierer Meinhardt system. In this research, it is concluded that the equilibrium point  which was initially stable when  becomes stable only when and .
Co-Authors Sutrima Sutrima