Blow-up and global solutions to L^p norm preserving non-local flows

Mathematics – Analysis of PDEs

Scientific paper

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10 pages

Scientific paper

In this paper, we study global existence and blow up properties to $L^p$ norm
preserving non-local heat flows. We first study two kinds of $L^p$ norm
preserving non-local flows and prove that these flows have the global
solutions. Finally, we give a example to show that one kind of this heat flow
may blow up in $L^{\infty}$ norm though its $L^p$ norm is preserved.

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