Traveling wave solutions for fully parabolic Keller-Segel chemotaxis systems with a logistic source
| dc.contributor.author | Salako, Rachidi | |
| dc.contributor.author | Shen, Wenxian | |
| dc.date.accessioned | 2021-09-29T18:19:30Z | |
| dc.date.available | 2021-09-29T18:19:30Z | |
| dc.date.issued | 2020-05-27 | |
| dc.description.abstract | This article concerns traveling wave solutions of the fully parabolic Keller-Segel chemotaxis system with logistic source, ut = Δu - X∇ ⋅ (u∇v) + u(α - bu), x ∈ ℝN, τvt = Δv - λv + μu, x ∈ ℝN, where X, μ, λ, α, b are positive numbers, and τ ≥ 0. Among others, it is proved that if b > 2Xμ and τ ≥ 1/2(1 - λ/α)+, then for every c ≥ 2√α, this system has a traveling wave solution (u, v)(t, x) = (Uτ,c(x ⋅ ξ - ct), Vτ,c(x ⋅ ξ - ct)) (for all ξ ∈ ℝN) connecting the two constant steady states (0, 0) and (α/b, μ/λ α/b), and there is no such solutions with speed c less than 2√α, which improves the results established in [30], and shows that this system has a minimal wave speed c*0 = 2√α, which is independent of the chemotaxis. | |
| dc.description.department | Mathematics | |
| dc.format | Text | |
| dc.format.extent | 18 pages | |
| dc.format.medium | 1 file (.pdf) | |
| dc.identifier.citation | Salako, R. B., & Shen, W. (2020). Traveling wave solutions for fully parabolic Keller-Segel chemotaxis systems with a logistic source. <i>Electronic Journal of Differential Equations, 2020</i>(53), pp. 1-18. | |
| dc.identifier.issn | 1072-6691 | |
| dc.identifier.uri | https://hdl.handle.net/10877/14560 | |
| dc.language.iso | en | |
| dc.publisher | Texas State University, Department of Mathematics | |
| dc.rights | Attribution 4.0 International | |
| dc.rights.uri | https://creativecommons.org/licenses/by/4.0/ | |
| dc.source | Electronic Journal of Differential Equations, 2020, San Marcos, Texas: Texas State University and University of North Texas. | |
| dc.subject | Parabolic chemotaxis system | |
| dc.subject | Logistic source | |
| dc.subject | Traveling wave solution | |
| dc.subject | Minimal wave speed | |
| dc.title | Traveling wave solutions for fully parabolic Keller-Segel chemotaxis systems with a logistic source | |
| dc.type | Article |