Boundedness in a quasilinear parabolic-parabolic chemotaxis system with nonlinear logistic source. (English) Zbl 1363.35195

Summary: We study a quasilinear parabolic-parabolic chemotaxis system with nonlinear logistic source, under homogeneous Neumann boundary conditions in a smooth bounded domain. By establishing proper a priori estimates we prove that, with both the diffusion function and the chemotaxis sensitivity function being positive, the corresponding initial boundary value problem admits a unique global classical solution which is uniformly bounded. The result of this paper is a generalization of that of X. Cao [J. Math. Anal. Appl. 412, No. 1, 181–188 (2014; Zbl 1364.35123)].


35K59 Quasilinear parabolic equations
92C17 Cell movement (chemotaxis, etc.)


Zbl 1364.35123
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