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{\sc Qualitative behavior of solutions to a class of Keller-Segel system}
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{\textsf{Monica Marras}}
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{Dipartimento di Matematica e Informatica,
Universit$\rm \grave{a}$ di Cagliari }
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We are interested in qualitative properties as blow-up phenomena, decay in time, boundedness, global existence to solutions of some classes of parabolic systems. In particular we consider a chemotaxis system with flux limitation in a bounded and smooth domain $\Omega \subset \mathbb{R}^N, \ \ N\geq 3$ and we show a criterion which ensure that, under suitable condition on data, the solution blows up in finite time in $L^{\infty}(\Omega)$ and for some $p>\frac N 2$ it also blows up in $L^p(\Omega)-norm$. Moreover we study the global existence and boundedness of the solution. |
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