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Global existence and boundedness of classical solutions for a chemotaxis model with logistic source

Baghaei, K ; Sharif University of Technology | 2013

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  1. Type of Document: Article
  2. DOI: 10.1016/j.crma.2013.07.027
  3. Publisher: 2013
  4. Abstract:
  5. We consider the chemotaxis system:. {ut=δu-∇;{dot operator}(uχ(v)∇;v)+f(u),x∈Ω,t>0,vt=δv-v+ug(u),x∈Ω,t>0, under homogeneous Neumann boundary conditions in a bounded domain Ω⊂Rn, n≥ 1, with smooth boundary and function f is assumed to generalize the logistic source:. f(u)=au-bu2,u≥0, with a>0,b>0. Moreover, χ( s) and g( s) are nonnegative smooth functions and satisfy:. χ(s)≤κ script(1+θ symbols)k,s≥0, with some κ script>0,θ symbol>0 and k>1,g(s)≤h0(1+hs)δ,s≥0,withh0>0,h≥0,δ≥0. We prove that for all positive values of κ script, a and b, classical solutions to the above system are uniformly-in-time bounded. This result extends a recent result by C. Mu, L. Wang, P. Zheng and Q. Zhang (2013) [13], which asserts the global existence and boundedness of classical solutions on condition that 0 ≤ a< 2. b and κ script be sufficiently small
  6. Keywords:
  8. Source: Comptes Rendus Mathematique ; Volume 351, Issue 15-16 , 2013 , Pages 585-591 ; 1631073X (ISSN)
  9. URL: http://www.sciencedirect.com/science/article/pii/S1631073X13001854