Construction of unique mild solution and continuity of solution for the small initial data to 1-D Keller-Segel system

Abstract

<p style='text-indent:20px;'>In this paper, a one-dimensional Keller-Segel system of parabolic-parabolic type which is defined on the bounded interval with the Dirichlet boundary condition is considered. Under the assumption that initial data is sufficiently small, a unique mild solution to the system is constructed and the continuity of solution for the initial data is shown, by using an argument of successive approximations.</p>