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Indexed by:期刊论文

Date of Publication:2019-08-01

Journal:ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK

Included Journals:SCIE、EI

Volume:70

Issue:4

ISSN No.:0044-2275

Key Words:Chemotaxis; Nonlinear signal production; Logistic-type source; Global boundedness; Fully parabolic

Abstract:This paper is concerned with the zero-flux logistic chemotaxis system with nonlinear signal production: ut=u-delta(u delta v)+f(u), vt=v-v+g(u) in a bounded and smooth domain < subset of>Rn (n1), where >0 is a constant, and f,gC1(R) generalize the prototypes f(s)=s-s and g(s)=s(s+1)-1 with >1 and ,>0. The existing studies, for the case that the self-diffusion or the logistic-type source prevails over the cross-diffusion singly, have asserted the global boundedness of solutions under the assumption that <, or <-1, or =-1 with >0 suitably large. In the present paper, we prove that if -1==, then due to the self-diffusion and the logistic kinetics working together, the solutions are globally bounded regardless of the size of >0. Note that -1== reduces to =2 and =1 if n=2. Hence, our result covers that of the two-dimensional classical chemotaxis system with logistic source: ut=u-delta(u delta v)+u-u2, vt=v-v+u (Osaki et al. in Nonlinear Anal 51:119-144, 2002).