Department of Mathematics
Zawia University, Zawia, Libya
email: aelagha46@gmail.com
Department of Mathematics
West Virginia University
Morgantown, WV 26506, USA
email: hhattori@wvu.edu
Aesha Lagha, Harumi Hattori
Abstract:
We study the existence of global solutions and their asymptotic behavior
for a chemotaxis system with chemo-attractant and repellent in three
dimensions. To accomplish this, we use the Fourier transform and energy
method. First, we establish Lq time-decay for the linear homogeneous
system using Fourier transform and finding Green's matrix. Then, we
find Lq time-decay for the nonlinear system using the Duhamel's
principle and the time-weighted estimates.
Submitted September 4, 2021. Published July 5, 2022.
Math Subject Classifications: 35Q31, 35Q35, 35Q92, 76N10.
Key Words: Energy method; a priori estimates; Fourier transform; time-decay rates.
DOI: https://doi.org/10.58997/ejde.2022.48
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| Aesha Lagha Department of Mathematics Zawia University, Zawia, Libya email: aelagha46@gmail.com | |
|
Harumi Hattori Department of Mathematics West Virginia University Morgantown, WV 26506, USA email: hhattori@wvu.edu |
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