Global solutions in a fully parabolic chemotaxis system with singular sensitivity |
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Authors: | Michael Winkler |
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Affiliation: | Fakult?t für Mathematik, Universit?t Duisburg‐Essen, 45117 Essen, Germany |
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Abstract: | The Neumann boundary value problem for the chemotaxis system is considered in a smooth bounded domain Ω??n, n?2, with initial data and v0∈W1, ∞(Ω) satisfying u0?0 and v0>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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Keywords: | chemotaxis global existence weak solutions singularity formation |
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