TY - JOUR
T1 - Controlled dynamics of a chemotaxis model with logarithmic sensitivity by physical boundary conditions
AU - Xue, Ling
AU - Zheng, Xiaoming
N1 - Funding Information:
from which we see that the principle part of (1.6) is hyperbolic in biologically relevant regimes (where the cellular density u > 0), provided χµ > 0. Hence, the analytical tools in hyperbolic balance laws become feasible for studying the qualitative behavior of the model. We focus on this case throughout the paper, since otherwise the characteristic fields may change the type, which could alter the dynamics of the model drastically. This is supported by the finite-time blowup of the explicit and numerical solutions constructed in [21].
Publisher Copyright:
© 2022 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
PY - 2022/10/17
Y1 - 2022/10/17
N2 - We study the global dynamics of large amplitude classical solutions to a system of balance laws, derived from a chemotaxis model with logarithmic sensitivity, subject to time-dependent boundary conditions. The model is supplemented with H2H2 initial data and unmatched boundary conditions at the endpoints of a one-dimensional interval. Under suitable assumptions on the boundary data, it is shown that classical solutions exist globally in time. Time asymptotically, the differences between the solutions and their corresponding boundary data converge to zero, as time goes to infinity. No smallness restrictions on the magnitude of the initial perturbations is imposed. Numerical simulations are carried out to explore some topics that are not covered by the analytical results.
AB - We study the global dynamics of large amplitude classical solutions to a system of balance laws, derived from a chemotaxis model with logarithmic sensitivity, subject to time-dependent boundary conditions. The model is supplemented with H2H2 initial data and unmatched boundary conditions at the endpoints of a one-dimensional interval. Under suitable assumptions on the boundary data, it is shown that classical solutions exist globally in time. Time asymptotically, the differences between the solutions and their corresponding boundary data converge to zero, as time goes to infinity. No smallness restrictions on the magnitude of the initial perturbations is imposed. Numerical simulations are carried out to explore some topics that are not covered by the analytical results.
UR - https://www.aimspress.com/article/doi/10.3934/era.2022230
M3 - Article
VL - 30
SP - 4530
EP - 4552
JO - Electronic Research Archive
JF - Electronic Research Archive
SN - 2688-1594
IS - 12
ER -