Abstract
In this paper, we study a simplified Othmer-Stevens model with reproduction term. By making use of a smart function transformation, the comparative method and some special mathematical analysis, we prove the existence of global, blow-up or quenching solutions of the problem on different conditions. More interesting results are reached. The result of the paper not only verifies a real biological phenomenon, but also provides a theoretical groundwork for numerical problems of the chemotaxis model.
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Foundation item: Supported by the National Natural Science Foundation of China(10471108)
Biography: CHEN Xueyong, male, Ph.D. candidate, research directions: partial differential equations and their applications.
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Chen, X., Liu, W. Behavior of the solutions to an othmer-stevens chemotaxis model with reproduction term. Wuhan Univ. J. Nat. Sci. 15, 277–282 (2010). https://doi.org/10.1007/s11859-010-0651-5
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DOI: https://doi.org/10.1007/s11859-010-0651-5