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The symmetry group of a centro-affine invariant flow is presented and a corresponding optimal system is found. Group invariant solutions associated to the optimal system are obtained and classified.  相似文献
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In this paper we study the long time behavior of the solution for a scalar nonlocal reaction-diffusion equation, in which the nonlocal term acts to conserve the spatial integral of the power of the unknown function as time evolves. A class of initial data is found to guarantee the existence of positive global solutions and the convergence to some steady states. A sufficient condition for positive global solutions to be unbounded is also given.  相似文献
3.
The length‐preserving nonlocal flow in the plane is investigated for locally convex closed curves, which may be non‐simple. It turns out that for certain classes of symmetric curves, the flows converge to m‐fold circles. Copyright © 2013 John Wiley & Sons, Ltd.  相似文献
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