Boundedness vs. blow-up in a chemotaxis system |
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Authors: | Dirk Horstmann Michael Winkler |
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Institution: | a Mathematisches Institut der Universität zu Köln, Weyertal 86-90, 50931 Köln, Germany b Lehrstuhl I für Mathematik der RWTH Aachen, Wüllnerstr. 5-7, 52056 Aachen, Germany |
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Abstract: | We determine the critical blow-up exponent for a Keller-Segel-type chemotaxis model, where the chemotactic sensitivity equals some nonlinear function of the particle density. Assuming some growth conditions for the chemotactic sensitivity function we establish an a priori estimate for the solution of the problem considered and conclude the global existence and boundedness of the solution. Furthermore, we prove the existence of solutions that become unbounded in finite or infinite time in that situation where this a priori estimate fails. |
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Keywords: | 35K50 35K57 35K60 92C17 |
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