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ABSTRACT This paper deals with the parabolic–elliptic chemotaxis-growth system with nonlinear secretion under homogeneous Neumann boundary conditions in a bounded domain with smooth boundary, where , a>0, b>0, r>1, and… Click to show full abstract
ABSTRACT This paper deals with the parabolic–elliptic chemotaxis-growth system with nonlinear secretion under homogeneous Neumann boundary conditions in a bounded domain with smooth boundary, where , a>0, b>0, r>1, and is a smooth function satisfying with some and . It is shown, either or or then the system admits a unique global bounded classical solution. Moreover, we obtain the large time behavior of the solution for a specific logistic source. Finally, for the case and r=k+1, large time behavior and convergence rate are established.
Journal Title: Applicable Analysis
Year Published: 2020
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