A hyperbolic-elliptic-elliptic system of an attraction-repulsion chemotaxis model with nonlinear productions

作者：Tian, Miaoqing^*; Hong, Liang; Zheng, Sining

来源：Journal of Evolution Equations, 2018, 18(2): 973-1001.

DOI：10.1007/s00028-018-0428-4

• Hyperbolic-elliptic-elliptic system
• Attraction-repulsion
• Nonlinear production
• Chemotaxis
• Logistic source
• Boundedness
• Blowup

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.

• 出版日期2018-6
• 单位大连理工大学; 辽宁大学; 郑州轻工业大学