The maximum principle for systems of parabolic equations subject to an avoidance set.
type: Item
instance of: scholarly article
title: The maximum principle for systems of parabolic equations subject to an avoidance set.
zbMATH Open document ID: 1049.35101
author: Bennett Chow
author: Peng Lu
published in: Pacific Journal of Mathematics
publication date: 2004-09-17T00:00:00Z
review text: 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. The authors 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.
Mathematics Subject Classification ID: 35K57
Mathematics Subject Classification ID: 53C44
Mathematics Subject Classification ID: 35B50
zbMATH DE Number: 2101150
zbMATH Keywords: Hamilton's maximum principle
zbMATH Keywords: avoidance set
reviewed by: Lubomira Softova
MaRDI profile type: Publication
full work available at URL: pjm.2004.214.201
OpenAlex ID: W2054138604
DOI: 10.2140/PJM.2004.214.201
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description: scientific article; zbMATH DE number 2101150