Open AccessGlobal existence and decay rates of the solutions for a chemotaxis system with Lotka-Volterra type model for chemoattractant and repellent
Author(s) -
Harumi Hattori,
Aesha Lagha
Publication year - 2021
Publication title -
discrete and continuous dynamical systems
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.289
H-Index - 70
eISSN - 1553-5231
pISSN - 1078-0947
DOI - 10.3934/dcds.2021071
Subject(s) - chemotaxis , homogeneous , type (biology) , fourier transform , mathematics , matrix (chemical analysis) , pure mathematics , mathematical analysis , combinatorics , materials science , biology , ecology , biochemistry , receptor , composite material
We study global existence and asymptotic behavior of the solutions for a chemotaxis system with chemoattractant and repellent in three dimensions. To accomplish this, we use the Fourier transform and energy method. We consider the case when the mass is conserved and we use the Lotka-Volterra type model for chemoattractant and repellent. Also, we establish \begin{document}$ L^q $\end{document} time-decay for the linear homogeneous system by using a Fourier transform and finding Green's matrix. Then, we find \begin{document}$ L^q $\end{document} time-decay for the nonlinear system using solution representation by Duhamel's principle and time-weighted estimates.