Lagha, AeshaHattori, Harumi2023-04-182023-04-182022-07-05Lagha, A., & Hattori, H. (2022). Cauchy problems for chemotaxis systems with chemo attractant and repellent. <i>Electronic Journal of Differential Equations, 2022</i>(48), pp. 1-23.1072-6691https://hdl.handle.net/10877/16607We 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.Text23 pages1 file (.pdf)enAttribution 4.0 InternationalEnergy methodA priori estimatesFourier transformTime-decay ratesArticle