## Journals

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### Open Access Journals

DCDS-B

We consider the asymptotic behavior of radially symmetric solutions of the aggregation equation
$ u_t = \nabla\cdot(u\nabla K*u) $ in $\mathbb{R}^n$,
for homogeneous potentials $K(x) = |x|^\gamma$, $\gamma>0$.
For $\gamma>2$, the aggregation happens in infinite time and
exhibits a concentration of mass along a collapsing $\delta$-ring.
We develop an asymptotic theory for the approach to this singular solution.
For $\gamma < 2$, the solution blows up in finite time and we present careful numerics of second
type similarity solutions for all $\gamma$ in this range, including
additional asymptotic behaviors in the limits $\gamma \to 0^+$ and $\gamma\to 2^-$.

DCDS-B

Studies of problems in fluid dynamics have spurred research in
many areas of mathematics, from rigorous analysis of nonlinear partial
differential equations, to numerical analysis, to modeling
and applied analysis of related physical systems.
This special issue of Discrete and Continuous Dynamical Systems Series B
is dedicated to our friend and colleague Tom Beale in recognition of
his important contributions to these areas.

For more information please click the "Full Text" above.

For more information please click the "Full Text" above.

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