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

The author is supported by JSPS KAKENHI Grant Number JP19K14558

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  • 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.

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


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