ASYMPTOTIC DYNAMICS OF A SYSTEM OF CONSERVATION LAWS FROM CHEMOTAXIS

作者：Zhu, Neng; Liu, Zhengrong; Wang, Fang; Zhao, Kun^*

来源：Discrete and Continuous Dynamical Systems, 2021, 41(2): 813-847.

DOI：10.3934/dcds.2020301

• Chemotaxis
• conservation laws
• Cauchy problem
• strong solutions
• global well-posedness
• long-time behavior
• explicit decay rates

This paper is devoted to the analytical study of the long-time asymptotic behavior of solutions to the Cauchy problem of a system of conservation laws in one space dimension, which is derived from a repulsive chemotaxis model with singular sensitivity and nonlinear chemical production rate. Assuming the H-2-norm of the initial perturbation around a constant ground state is finite and using energy methods, we show that there exists a unique global-in-time solution to the Cauchy problem, and the constant ground state is globally asymptotically stable. In addition, the explicit decay rates of the solutions to the chemically diffusive and non-diffusive models are identified under different exponent ranges of the nonlinear chemical production function.

• 单位
  长沙理工大学; 南昌大学