Construction of a unique mild solution of one-dimensional Keller-Segel systems with uniformly elliptic operators having variable coefficients

A one-dimensional Keller-Segel system which is defined through uniformly elliptic operators having variable coefficients is considered. In the main theorems, the local existence and uniqueness of the mild solution of the system are proved. The main method to construct the mild solution is an argument of successive approximations by means of strongly continuous semi-groups. (C)2018 Mathematical Institute Slovak Academy of Sciences