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| The Behavior of Solutions of Multidimensional Aggregation Equations with Mildly Singular Interaction Kernels |
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Citation： |
Andrea L. BERTOZZI,Thomas LAURENT.The Behavior of Solutions of Multidimensional Aggregation Equations with Mildly Singular Interaction Kernels[J].Chinese Annals of Mathematics B,2009,30(5):463~482 |
| Page view： 2172
Net amount： 1184 |
Authors： |
Andrea L. BERTOZZI; Thomas LAURENT; |
Foundation： |
the Office of Naval Research, the Army Research Office and the National Science
Foundation (No. DMS-0907931). |
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| Abstract： |
The authors consider the multidimensional aggregation equation
$\pa_t\rho-\div(\rho\nb\! K*\rho)=0$ in which the radially symmetric
attractive interaction kernel has a mild singularity at the origin
(Lipschitz or better), and review recent results on this problem
concerning well-posedness of nonnegative solutions and finite time
blowup in multiple space dimensions depending on the behavior of the
kernel at the origin. The problem with bounded initial data, data in
$L^p\cap L^1$, and measure solutions are also considered. |
Keywords： |
Well-posedness, Blowup, Osgood condition |
Classification： |
35Q80, 35Q35 |
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