Release Time:2019-03-12  Hits:

Indexed by: Journal Article

Date of Publication: 2018-06-01

Journal: JOURNAL OF EVOLUTION EQUATIONS

Included Journals: SCIE

Volume: 18

Issue: 2

Page Number: 973-1001

ISSN: 1424-3199

Key Words: Hyperbolic-elliptic-elliptic system; Attraction-repulsion; Nonlinear production; Chemotaxis; Logistic source; Boundedness; Blowup

Abstract: 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.