Journal article
The Existence of Moving Spike Patterns in an Attractive Chemotaxis Model
Mathematical methods in the applied sciences, Vol.48(14), pp.13505-13516
09/30/2025
DOI: 10.1002/mma.11118
Appears in UI Libraries Support Open Access
Abstract
We prove rigorously the existence of moving spike patterns in an attractive chemotaxis model with small diffusion coefficient for the chemical. In the zero diffusion limit, 𝜖 → 0, we prove that the non-monotone traveling wave solutions of the system with 𝜖 > 0 converge to those of the system with 𝜖 = 0. Moreover, we show that the traveling wave solutions are linearly unstable. We perform numerical simulations and find existence of the moving spike patterns when 𝜖 > 0. We confirm that as 𝜖 → 0 the traveling wave solutions of the system with 𝜖 > 0 converge to the traveling wave solutions of the system with 𝜖 = 0.
Details
- Title: Subtitle
- The Existence of Moving Spike Patterns in an Attractive Chemotaxis Model
- Creators
- Tong Li - University of IowaCasey Stone - University of Iowa
- Resource Type
- Journal article
- Publication Details
- Mathematical methods in the applied sciences, Vol.48(14), pp.13505-13516
- DOI
- 10.1002/mma.11118
- ISSN
- 0170-4214
- eISSN
- 1099-1476
- Publisher
- Wiley
- Grant note
- Erwin and Peggy Kleinfeld Graduate Fellowship fund at The University of IowaErwin and Peggy Kleinfeld Graduate Fellowship fundUniversity of Iowa Graduate CollegeProfessional Development Award
Casey Stone acknowledges support from the Erwin and Peggy Kleinfeld Graduate Fellowship fund. She would also like to thank the University of Iowa Graduate College for the Post-Comprehensive Exam Fellowship awarded for the Spring 2024 semester. Tong Li thanks the support of a Professional Development Award and an Obermann Fellow for the Fall 2023, The University of Iowa.
- Language
- English
- Electronic publication date
- 2025
- Date published
- 09/30/2025
- Academic Unit
- Mathematics
- Record Identifier
- 9984832183602771
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