Large time behavior and diffusion limit for a system of balance laws from chemotaxis in multi-dimensions
Large time behavior and diffusion limit for a system of balance laws from chemotaxis in multi-dimensions
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DOI：
10.4310/cms.2021.v19.n1.a10
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发表时间：
2020-08
期刊：
影响因子：
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通讯作者：
Tong Li;Dehua Wang;Fang Wang;Zhian Wang;Kun Zhao
中科院分区：
文献类型：
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作者：
Tong Li;Dehua Wang;Fang Wang;Zhian Wang;Kun Zhao
考虑了多维空间中由奇异灵敏度趋化模型导出的平衡律系统的柯西问题。利用能量方法，首先证明了当初始数据的一阶空间导数的能量足够小时，柯西问题经典解的全局适定性，并证明了当时间趋于无穷时，解收敛于规定的常数平衡态。然后证明了当化学扩散系数趋于零时，完全耗散模型的解收敛于相应的部分耗散模型的解。
We consider the Cauchy problem for a system of balance laws derived from a chemotaxis model with singular sensitivity in multiple space dimensions. Utilizing energy methods, we first prove the global well-posedness of classical solutions to the Cauchy problem when only the energy of the first order spatial derivatives of the initial data is sufficiently small, and the solutions are shown to converge to the prescribed constant equilibrium states as time goes to infinity. Then we prove that the solutions of the fully dissipative model converge to those of the corresponding partially dissipative model when the chemical diffusion coefficient tends to zero.