Boundedness in the Higher-Dimensional Parabolic-Parabolic Chemotaxis System with Logistic Source

Shakerian, Shaya | 2011

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 43079 (02)
  4. University: Sharif University of Technology
  5. Department: Mathematical Sciences
  6. Advisor(s): Hesaaraki, Mahmoud
  7. Abstract:
  8. We Consider the Chemotaxi Systems in a smooth bounded domain as follow:{ █(ut = Δu-χ∇.(u∇v)+ f (u) x ϵ Ω ,t>0 @ @τ vt =Δv-v+u x ϵ Ω ,t>0)┤ Where χ∈ and f(u) =Au - Buα generalizes the logistic function with A≥0, B>0 and α>1. First for τ=0, global existence of such solutions for any nonnegative initial data is proved under the assumption that . Moreover, boundedness properties of the constructed solutions are studied. Next we assume that 2=α, τ>0 and we consider nonnegative solutions of the Neumann
    Boundary value problem for the chemotaxis system above in a smooth bounded convex domain . We will see that if B is sufficiently large then for all sufficiently smooth initial data the problem possesses a unique global-in-time classical solution that is bounded
  9. Keywords:
  10. Global Existence ; Chemotaxis ; Logistic Source ; Boundedness ; Absorbing Set

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