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Logistic type attraction-repulsion chemotaxis systems with a free boundary or unbounded boundary. I. Asymptotic dynamics in fixed unbounded domain

  • * Corresponding author: Lianzhang Bao

    * Corresponding author: Lianzhang Bao 

The first author is supported by China Postdoctoral Science Foundation (183816). The second author is supported by NSF grant DMS–1645673

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  • The current series of research papers is to investigate the asymptotic dynamics in logistic type chemotaxis models in one space dimension with a free boundary or an unbounded boundary. Such a model with a free boundary describes the spreading of a new or invasive species subject to the influence of some chemical substances in an environment with a free boundary representing the spreading front. In this first part of the series, we investigate the dynamical behaviors of logistic type chemotaxis models on the half line $ \mathbb{R}^+ $, which are formally corresponding limit systems of the free boundary problems. In the second of the series, we will establish the spreading-vanishing dichotomy in chemoattraction-repulsion systems with a free boundary as well as with double free boundaries.

    Mathematics Subject Classification: Primary: 35R35, 35J65, 35K20; Secondary: 92B05.


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