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December  2013, 18(10): 2647-2668. doi: 10.3934/dcdsb.2013.18.2647

Well-posedness for a model of individual clustering

Elissar Nasreddine 1,

1. 

Institut de Mathématiques de Toulouse, Université de Toulouse, F-31062 Toulouse cedex 9

Received  November 2012 Revised  February 2013 Published  October 2013

We study the well-posedness of a model of individual clustering. Given $p>N\geq 1$ and an initial condition in $W^{1,p}(\Omega)$, the local existence and uniqueness of a strong solution is proved. We next consider two specific reproduction rates and show global existence if $N=1$, as well as, the convergence to steady states for one of these rates.
Keywords: compactness method., steady state, global existence, Elliptic system, local existence.
Mathematics Subject Classification: 35K20, 35B40, 35M33, 35J47, 35Q9.
Citation: Elissar Nasreddine. Well-posedness for a model of individual clustering. Discrete & Continuous Dynamical Systems - B, 2013, 18 (10) : 2647-2668. doi: 10.3934/dcdsb.2013.18.2647
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show all references

References:
[1]

Oxford Lecture Series in Mathematics and it Applications, 2006. Google Scholar

[2]

Parabolic and Navier-Stokes Equations, Part 1, 105-117, Banach Center Publ., 81, Part 1, Polish Acad. Sci. Inst. Math., Warsaw, 2008. doi: 10.4064/bc81-0-7.  Google Scholar

[3]

J. Math. Anal. Appl., 67 (1979), 525-541. doi: 10.1016/0022-247X(79)90041-6.  Google Scholar

[4]

Bolletino, U. M. I.(5), 16 (1979), 22-31.  Google Scholar

[5]

J. Math. Biol., 26 (1988), 651-660. doi: 10.1007/BF00276146.  Google Scholar

[6]

Providence (R. I.) , American Mathematical Society, 1988. Google Scholar

[7]

Nonlinear Anal., 9 (1985), 321-333. doi: 10.1016/0362-546X(85)90057-4.  Google Scholar

[8]

(French) Ann. Fac. Sci. Toulouse Math. (5), 2 (1980), 125-135. doi: 10.5802/afst.550.  Google Scholar

[9]

Annali di Mathematica Pura ed Applicata (IV), 146 (1987), 65-69. doi: 10.1007/BF01762360.  Google Scholar

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