Abstract
A logarithmic model type chemotaxis equation is introduced with porous medium diffusion and a population dependent consumption rate. The classical assumption that individual bacterium can sense the chemical gradient is not taken. Instead, the chemotactic term appears by assuming that the migration distance is inversely proportional to the amount of food if food is the reason for migration. The existence and uniqueness of a traveling wave solution of the model are obtained. In particular, solutions have interfaces that divide into constant and non-constant regions. In particular, the profile of the population distribution has compact support. Numerical simulations are provided and compared with analytic results.
Original language | English |
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Article number | 124090 |
Journal | Journal of Mathematical Analysis and Applications |
Volume | 488 |
Issue number | 2 |
DOIs | |
Publication status | Published - 15 Aug 2020 |
Bibliographical note
Publisher Copyright:© 2020 Elsevier Inc.
Keywords
- Chemotaxis
- Compact support
- Food metric
- Porous medium diffusion
- Traveling wave