In this paper,we study long-time dynamics and diffusion limit of large-data solutions to a system of balance laws arising from a chemotaxis model with logarithmic sensitivity and nonlinear production/degradation rate....In this paper,we study long-time dynamics and diffusion limit of large-data solutions to a system of balance laws arising from a chemotaxis model with logarithmic sensitivity and nonlinear production/degradation rate.Utilizing energy methods,we show that under time-dependent Dirichlet boundary conditions,long-time dynamics of solutions are driven by their boundary data,and there is no restriction on the magnitude of initial energy.Moreover,the zero chemical diffusivity limit is established under zero Dirichlet boundary conditions,which has not been observed in previous studies on related models.展开更多
基金partially supported by China Scholarship Council(No.201906150159)partially supported by China Scholarship Council(No.201906150101)+2 种基金National Natural Science Foundation of China(No.11971176,No.11871226)partially supported by Fundamental Research Funds for the Central Universities of China(No.3072020CFT2402)partially supported by Simons Foundation Collaboration Grant for Mathematicians(No.413028)。
文摘In this paper,we study long-time dynamics and diffusion limit of large-data solutions to a system of balance laws arising from a chemotaxis model with logarithmic sensitivity and nonlinear production/degradation rate.Utilizing energy methods,we show that under time-dependent Dirichlet boundary conditions,long-time dynamics of solutions are driven by their boundary data,and there is no restriction on the magnitude of initial energy.Moreover,the zero chemical diffusivity limit is established under zero Dirichlet boundary conditions,which has not been observed in previous studies on related models.
