Open AccessConstruction of unique mild solution and continuity of solution for the small initial data to 1-D Keller-Segel system
Author(s) -
Yumi Yahagi
Publication year - 2022
Publication title -
discrete and continuous dynamical systems. series b
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.864
H-Index - 53
eISSN - 1553-524X
pISSN - 1531-3492
DOI - 10.3934/dcdsb.2021099
Subject(s) - interval (graph theory) , mathematics , bounded function , dirichlet distribution , dirichlet boundary condition , mathematical analysis , type (biology) , boundary (topology) , boundary value problem , combinatorics , geology , paleontology
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.