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<p>This paper is concerned with a three-component cross-diffusion system, which was proposed by Albi, Artina, Foransier and Markowich to model the ion transport networks. This system shares some basic features with the two-component repulsive chemotaxis system, although it also contains a possible singularity and a stronger nonlinearity, which may enhance explosion-supporting properties. The intention of this paper is to find a new type of small initial data which ensures the global existence of classical solution of the corresponding Dirichlet initial-boundary value problem in the two-dimensional setting. Moreover, the boundedness of solution is obtained as well.</p>

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Classical Solvability in a 2-D Cross-Diffusion System Arising from the Ion Transport Networks

  • 期刊论文

  • 发表日期：

    2025年5月15日

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  • Jieqiong Shen

摘要

This paper is concerned with a three-component cross-diffusion system, which was proposed by Albi, Artina, Foransier and Markowich to model the ion transport networks. This system shares some basic features with the two-component repulsive chemotaxis system, although it also contains a possible singularity and a stronger nonlinearity, which may enhance explosion-supporting properties. The intention of this paper is to find a new type of small initial data which ensures the global existence of classical solution of the corresponding Dirichlet initial-boundary value problem in the two-dimensional setting. Moreover, the boundedness of solution is obtained as well.