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The maximum principle
for systems of parabolic equations subject to an avoidance
set
Bennett Chow and Peng Lu |
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Vol. 214 (2004), No. 2, 201–222
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Abstract |
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Hamilton’s maximum principle for systems states that given a reaction-diffusion equation (semi-linear heat-type equation) for sections of a vector bundle over a manifold, if the solution is initially in a subset invariant under parallel translation and convex in the fibers and if the ODE associated to the PDE preserves the subset, then the solution remains in the subset for positive time. We generalize this result to the case where the subsets are time-dependent and where there is an avoidance set from which the solution is disjoint. In applications the existence of an avoidance set can sometimes be used to prove the preservation of a subset of the vector bundle by the PDE. |
Milestones
Received: 29 May 2002
Revised: 5 August 2003
Published: 1 April 2004
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Authors |
| Bennett Chow | |
| Department of Mathematics University of California, San Diego La Jolla, CA 92093 |
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| Peng Lu | |
| Department of Mathematics and
Statistics McMaster University Hamilton, Ontario Canada, L8S 4K1 |
Department of Mathematics University of Oregon Eugene, OR 97403 |
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