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论文类型：期刊论文

发表时间：2018-06-01

发表刊物：JOURNAL OF EVOLUTION EQUATIONS

收录刊物：SCIE

卷号：18

期号：2

页面范围：973-1001

ISSN号：1424-3199

关键字：Hyperbolic-elliptic-elliptic system; Attraction-repulsion; Nonlinear production; Chemotaxis; Logistic source; Boundedness; Blowup

摘要：This paper studies the hyperbolic-elliptic-elliptic system of an attraction-repulsion chemotaxis model with nonlinear productions and logistic source: , , , in a bounded domain , , subject to the non-flux boundary condition. We at first establish the local existence of solutions (the so-called strong -solutions, satisfying the hyperbolic equation weakly and solving the elliptic ones classically) to the model via applying the viscosity vanishing method and then give criteria on global boundedness versus finite- time blowup for them. It is proved that if the attraction is dominated by the logistic source or the repulsion with , the solutions would be globally bounded; otherwise, the finite-time blowup of solutions may occur whenever . Under the balance situations with , or , the boundedness or possible finite-time blowup would depend on the sizes of the coefficients involved.