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

Yumi Yahagi | Zendy

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Construction 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 - 2021

Publication title -

discrete and continuous dynamical systems - 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.

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