Flow invariance for perturbed nonlinear evolution equations.
Bothe, Dieter (1996)
Abstract and Applied Analysis
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Bothe, Dieter (1996)
Abstract and Applied Analysis
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Marek Fila, Ján Filo (1989)
Mathematica Slovaca
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Piotr Biler, Grzegorz Karch, Wojbor A Woyczyński (2001)
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Calsina, Angel, Solà-Morales, Joan, València, Marta
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Aylaj, B., Achhab, M.E., Laabissi, M. (2008)
Abstract and Applied Analysis
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M. Pierre, R. Texier-Picard (2009)
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Marek Fila, Ján Filo (1988)
Commentationes Mathematicae Universitatis Carolinae
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Takayoshi Ogawa (2006)
Banach Center Publications
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We classify the global behavior of weak solutions of the Keller-Segel system of degenerate and nondegenerate type. For the stronger degeneracy, the weak solution exists globally in time and has a uniform time decay under some extra conditions. If the degeneracy is weaker, the solution exhibits a finite time blow up if the data is nonnegative. The situation is very similar to the semilinear case. Some additional discussion is also presented.