Commun. Math. Anal. Appl., 1 (2022), pp. 319-344.
Published online: 2022-03
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In this paper, we consider a new type of chemotaxis model with acceleration, which assumes that the advective acceleration, instead of velocity in the classical chemotaxis model, of species is proportional to the chemical signal concentration gradient. This new model has an additional equation governing the velocity field with more delicate boundary conditions. We show that this new type of chemotaxis model with acceleration precludes the blow-up and admits globally bounded solutions in two and three dimensions, in contrast to the classical chemotaxis models which may have blow-up in three dimensions or in two dimensions with a critical mass. Moreover, we numerically illustrate that this new type of chemotaxis model can typically generate aggregation patterns. Some open questions are discussed for further studies.
}, issn = {2790-1939}, doi = {https://doi.org/10.4208/cmaa.2022-0003}, url = {http://global-sci.org/intro/article_detail/cmaa/20310.html} }In this paper, we consider a new type of chemotaxis model with acceleration, which assumes that the advective acceleration, instead of velocity in the classical chemotaxis model, of species is proportional to the chemical signal concentration gradient. This new model has an additional equation governing the velocity field with more delicate boundary conditions. We show that this new type of chemotaxis model with acceleration precludes the blow-up and admits globally bounded solutions in two and three dimensions, in contrast to the classical chemotaxis models which may have blow-up in three dimensions or in two dimensions with a critical mass. Moreover, we numerically illustrate that this new type of chemotaxis model can typically generate aggregation patterns. Some open questions are discussed for further studies.