TY - JOUR
T1 - On a New Type of Chemotaxis Model with Acceleration
AU - Tao , Weirun
AU - Wang , Zhi-An
JO - Communications in Mathematical Analysis and Applications
VL - 2
SP - 319
EP - 344
PY - 2022
DA - 2022/03
SN - 1
DO - http://doi.org/10.4208/cmaa.2022-0003
UR - https://global-sci.org/intro/article_detail/cmaa/20310.html
KW - Chemotaxis, acceleration, global boundedness, global stability, pattern formation.
AB - <p style="text-align: justify;">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.</p>