Work

Dynamical behaviour of a logarithmically sensitive chemotaxis model under time-dependent boundary conditions

Year: 2024

Type: article

Abstract: This article studies the dynamical behaviour of classical solutions of a hyperbolic system of balance laws, derived from a chemotaxis model with logarithmic sensitivity, with time-dependent boundary conditions. It is shown that under suitable assumptions on the boundary data, solutions starting in the $H^2$ -space exist globally in time and the differences between the solutions and their corresponding boundary data converge to zero as time goes to infinity. There is no smallness restriction on the magnitude of the initial perturbations. Moreover, numerical simulations show that the assumptions on the boundary data are necessary for the above-mentioned results to hold true. In addition, numerical results indicate that the solutions converge asymptotically to time-periodic states if the boundary data are time-periodic.

Source: European Journal of Applied Mathematics

DOI: 10.1017/s0956792524000329

Authors: Padi Fuster Aguilera, Kun Zhao

Institutions: University of Colorado Boulder, Tulane University, Harbin Engineering University

Language: English

Topic: Mathematical Biology Tumor Growth

Subfield: Modeling and Simulation

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $3,450

Funder: National Science Foundation