Asymptotic Profile Of The Steady State Solution Of A Chemotaxis Model With Singular Sensitivity

This paper is concerned with the steady state problem of a chemotaxis model with singular sensitivity in one dimensional spatial domain.First,We transform the steady state problem into an algebraic system with equivalent solvability,then parameterize the solution of the algebraic system,and obtain the existence of the positive monotone nonconstant steady state solution of the steady state problem,and discuss the uniqueness of the steady state solution.In addition,we also obtained the asymptotic profile of the steady state solution when the ratio k of the chemotactic coefficient to the bacterial diffusion coefficient approaches infinity.The results show that as k approaches infinity,the bacterial population density function forms a spike.