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PERSISTENCE OF TRAVELING WAVES TO THE TIME FRACTIONAL KELLER-SEGEL SYSTEM WITH A SMALL PARAMETER
  • Shuting Chen,
  • Jinde Cao,
  • Ivanka Stamova
Shuting Chen
Southeast University
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Jinde Cao
Southeast University

Corresponding Author:jdcao@seu.edu.cn

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Ivanka Stamova
The University of Texas at San Antonio
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Abstract

This paper aims to investigate the time fractional Keller-Segel system with a small parameter. After the fractional order traveling wave transformation, the heteroclinic orbit to the degenerate time fractional Keller-Segel system is demonstrated through the method of constructing a suitable invariant region. Moreover, the persistence of traveling waves in the system with a small parameter can be further illustrated. The results are mainly reliance on the application of geometric singular perturbation theory and Fredholm theorem, which are fundamental theoretical frameworks for dealing with problems of complexity and high dimensionality. Eventually, the asymptotic behavior is depicted by the asymptotic theory to illustrate the rate of decay for traveling waves.
17 Feb 2023Submitted to Mathematical Methods in the Applied Sciences
17 Feb 2023Submission Checks Completed
17 Feb 2023Assigned to Editor
24 Feb 2023Review(s) Completed, Editorial Evaluation Pending
26 Feb 2023Reviewer(s) Assigned
30 Apr 2023Editorial Decision: Revise Minor
04 May 20231st Revision Received
05 May 2023Submission Checks Completed
05 May 2023Assigned to Editor
05 May 2023Review(s) Completed, Editorial Evaluation Pending
09 May 2023Reviewer(s) Assigned
12 Jun 2023Editorial Decision: Accept