Global solutions in a fully parabolic chemotaxis system with singular sensitivity | Zendy

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Global solutions in a fully parabolic chemotaxis system with singular sensitivity

Author(s) -

Winkler Michael

Publication year - 2010

Publication title -

mathematical methods in the applied sciences

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.719

H-Index - 65

eISSN - 1099-1476

pISSN - 0170-4214

DOI - 10.1002/mma.1346

Subject(s) - mathematics , bounded function , neumann boundary condition , domain (mathematical analysis) , chemotaxis , mathematical analysis , range (aeronautics) , boundary value problem , sensitivity (control systems) , boundary (topology) , electronic engineering , engineering , materials science , composite material , biochemistry , chemistry , receptor

The Neumann boundary value problem for the chemotaxis systemis considered in a smooth bounded domain Ω⊂ℝ n , n ⩾2, with initial data and v 0 ∈ W 1, ∞ (Ω) satisfying u 0 ⩾0 and v 0 >0 in . It is shown that if then for any such data there exists a global‐in‐time classical solution, generalizing a previous result which asserts the same for n =2 only. Furthermore, it is seen that the range of admissible χ can be enlarged upon relaxing the solution concept. More precisely, global existence of weak solutions is established whenever . Copyright © 2010 John Wiley & Sons, Ltd.

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