Dimension prints and the avoidance of sets for flow solutions of non-autonomous ordinary differential equations
Robinson, James and Sharples, Nicholas ORCID: https://orcid.org/0000-0003-1722-5647
(2013)
Dimension prints and the avoidance of sets for flow solutions of non-autonomous ordinary differential equations.
Journal of Differential Equations, 254
.
pp. 4144-4167.
ISSN 0022-0396
[Article]
(doi:10.1016/j.jde.2013.02.012)
|
PDF
- Final accepted version (with author's formatting)
Download (287kB) | Preview |
Abstract
We provide a criterion for a generalised flow solution of a non-autonomous 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 box-counting dimension. We define the r-codimension 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 r-codimension 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: | 30 Nov 2022 00:12 |
URI: | https://eprints.mdx.ac.uk/id/eprint/18182 |
Actions (login required)
![]() |
View Item |
Statistics
Additional statistics are available via IRStats2.