Please use this identifier to cite or link to this item:
http://hdl.handle.net/10397/95573
Title: | Nonlinear stability of strong traveling waves for the singular Keller–Segel system with large perturbations | Authors: | Peng, H Wang, ZA |
Issue Date: | 15-Sep-2018 | Source: | Journal of differential equations, 15 Sept. 2018, v. 265, no. 6, p. 2577-2613 | Abstract: | This paper is concerned with the nonlinear stability of traveling wave solutions for a conserved system of parabolic equations derived from a singular chemotaxis model describing the initiation of tumor angiogenesis. When the initial datum is a continuous small perturbation with zero integral from the spatially shifted traveling wave, the asymptotic stability of the large-amplitude (strong) traveling waves has been established in a series of works [29,34,35] by the second author with his collaborators. In this paper, we shall show that similar stability results indeed hold true for large and discontinuous initial data (i.e. the initial perturbation from the traveling wave could be discontinuous and has large oscillations) such as Riemann data with large jumps. To the best of our knowledge, this paper provides a first result on the asymptotic stability of large-amplitude traveling waves with large initial perturbation for a system of conservation laws, although similar results have been available for the scalar equations (cf. [8,42]). We also extend existing results to the initial data with lower regularity. | Keywords: | Chemotaxis Traveling wave solutions Nonlinear stability Logarithmic sensitivity Large perturbation Discontinuous data |
Publisher: | Academic Press | Journal: | Journal of differential equations | ISSN: | 0022-0396 | EISSN: | 1090-2732 | DOI: | 10.1016/j.jde.2018.04.041 | Rights: | © 2018 Elsevier Inc. All rights reserved. © 2018. This manuscript version is made available under the CC-BY-NC-ND 4.0 license https://creativecommons.org/licenses/by-nc-nd/4.0/ The following publication Peng, H., & Wang, Z. A. (2018). Nonlinear stability of strong traveling waves for the singular Keller–Segel system with large perturbations. Journal of Differential Equations, 265(6), 2577-2613 is available at https://doi.org/10.1016/j.jde.2018.04.041. |
Appears in Collections: | Journal/Magazine Article |
Files in This Item:
File | Description | Size | Format | |
---|---|---|---|---|
Peng_Nonlinear_Stability_Strong.pdf | Pre-Published version | 746.86 kB | Adobe PDF | View/Open |
Page views
64
Last Week
0
0
Last month
Citations as of Sep 22, 2024
Downloads
22
Citations as of Sep 22, 2024
SCOPUSTM
Citations
13
Citations as of Sep 26, 2024
WEB OF SCIENCETM
Citations
13
Citations as of Sep 26, 2024
Google ScholarTM
Check
Altmetric
Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.