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

Yumi Yahagi

doi:10.3934/dcdsb.2021099

Article Contents

2022, Volume 27, Issue 3: 1497-1510. Doi: 10.3934/dcdsb.2021099

This issue Previous Article The dynamic properties of a generalized Kawahara equation with Kuramoto-Sivashinsky perturbation Next Article Variational problems associated with a system of nonlinear Schrödinger equations with three wave interaction

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

Yumi Yahagi

Department of Mathematical Informatics, Tokyo University of Information Sciences, 4-1 Onaridai, Wakaba-ku, Chiba, 265-8501 Japan

Received: October 2020

Revised: January 2021

Early access: March 2021

Published: March 2022

The author is supported by JSPS KAKENHI Grant Number JP19K14558

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Abstract

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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Mathematics Subject Classification: Primary: 35A01, 35A02; Secondary: 35B30.

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References

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