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Global solutions in a fully parabolic chemotaxis system with singular sensitivity

✍ Scribed by Michael Winkler

Publisher
John Wiley and Sons
Year
2010
Tongue
English
Weight
239 KB
Volume
34
Category
Article
ISSN
0170-4214

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✦ Synopsis

Communicated by Howard A. Levine

The Neumann boundary value problem for the chemotaxis system ⎧ ⎨

⎩

is considered in a smooth bounded domain X βŠ‚ R n , n 2, with initial data u 0 ∈ C 0 ( X) and v 0 ∈ W 1,∞ (X) satisfying u 0 0 and v 0 >0 in X. It is shown that if 0<v< √ 2 / n 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 v can be enlarged upon relaxing the solution concept. More precisely, global existence of weak solutions is established whenever 0<v< √ (n+2) / (3n-4).

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