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.

中文翻译：

---

趋化性守恒律系统的渐近动力学

本文致力于一维空间守恒律系统柯西问题解的长期渐近行为的分析研究，该问题来自具有奇异敏感性和非线性化学生产率的排斥趋化模型。假设围绕恒定基态的初始扰动的$ H ^ 2 $范数是有限的，并且使用能量方法，我们证明了柯西问题存在唯一的全局及时解，并且恒定基态是全局的渐近稳定。另外，在非线性化学生产函数的不同指数范围内，确定了化学扩散模型和非扩散模型的解的显式衰减率。