Dimension prints and the avoidance of sets for flow solutions of nonautonomous ordinary differential equations
Robinson, James and Sharples, Nicholas (2013) Dimension prints and the avoidance of sets for flow solutions of nonautonomous ordinary differential equations. Journal of Differential Equations, 254 . pp. 41444167.

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Abstract
We provide a criterion for a generalised
ow solution of a nonautonomous
ordinary differential equation to avoid a subset of the phase space. This
improves on that established by Aizenman for the autonomous case, where
avoidance is guaranteed if the underlying vector field is sufficiently regular
and the subset has sufficiently small boxcounting dimension. We define the
rcodimension print of a subset $S\subset \R^{n}\times [0,T]$, which is a subset of $(0,\infty]^{2}$ that encodes the dimension of S in a way that distinguishes spatial and temporal detail. We prove that the subset S is avoided by a generalised flow solution with underlying vector field in $L^{p}(0, T; L^{q}(R^{n}))$ if the Holder conjugates (q^{*}; p^{*}) are in the rcodimension print of S.
Item Type:  Article 

Research Areas:  A. > School of Science and Technology 
Item ID:  18182 
Depositing User:  Nicholas Sharples 
Date Deposited:  15 Oct 2015 16:55 
Last Modified:  13 Oct 2016 14:37 
URI:  http://eprints.mdx.ac.uk/id/eprint/18182 
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