The parabolic-parabolic Keller-Segel equation
نویسندگان
چکیده
منابع مشابه
On the parabolic-elliptic limit of the doubly parabolic Keller–Segel system modelling chemotaxis
We establish new convergence results, in strong topologies, for solutions of the parabolic-parabolic Keller–Segel system in the plane, to the corresponding solutions of the parabolic-elliptic model, as a physical parameter goes to zero. Our main tools are suitable space-time estimates, implying the global existence of slowly decaying (in general, nonintegrable) solutions for these models, under...
متن کاملLarge mass self-similar solutions of the parabolic-parabolic Keller-Segel model of chemotaxis.
In two space dimensions, the parabolic-parabolic Keller-Segel system shares many properties with the parabolic-elliptic Keller-Segel system. In particular, solutions globally exist in both cases as long as their mass is less than a critical threshold M(c). However, this threshold is not as clear in the parabolic-parabolic case as it is in the parabolic-elliptic case, in which solutions with mas...
متن کاملA pr 2 00 8 On the parabolic - elliptic limit of the doubly parabolic Keller – Segel system modelling chemotaxis
We establish new convergence results, in strong topologies, for solutions of the parabolic-parabolic Keller–Segel system in the plane, to the corresponding solutions of the parabolic-elliptic model, as a physical parameter goes to zero. Our main tools are suitable space-time estimates, implying the global existence of slowly decaying (in general, nonintegrable) solutions for these models, under...
متن کاملAsymptotic estimates for the parabolic-elliptic Keller-Segel model in the plane
We investigate the large-time behavior of the solutions of the two-dimensional Keller-Segel system in self-similar variables, when the total mass is subcritical, that is less than 8π after a proper adimensionalization. It was known from previous works that all solutions converge to stationary solutions, with exponential rate when the mass is small. Here we remove this restriction and show that ...
متن کاملOn the parabolic-elliptic Patlak-Keller-Segel system in dimension 2 and higher
This review is dedicated to recent results on the 2d parabolic-elliptic PatlakKeller-Segel model, and on its variant in higher dimensions where the diffusion is of critical porous medium type. Both of these models have a critical mass Mc such that the solutions exist globally in time if the mass is less than Mc and above which there are solutions which blowup in finite time. The main tools, in ...
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ژورنال
عنوان ژورنال: Séminaire Laurent Schwartz — EDP et applications
سال: 2014
ISSN: 2266-0607
DOI: 10.5802/slsedp.76