Extended weak maximum principles for parabolic partial differential inequalities on unbounded domains

J. C. Meyer, D. J. Needham*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

8 Citations (Scopus)
120 Downloads (Pure)

Abstract

In this paper, we establish extended maximum principles for solutions to linear parabolic partial differential inequalities on unbounded domains, where the solutions satisfy a variety of growth/decay conditions on the unbounded domain. We establish a conditional maximum principle, which states that a solution u to a linear parabolic partial differential inequality satisfies a maximum principle whenever a suitable weight function can be exhibited. Our extended maximum principles are then established by exhibiting suitable weight functions and applying the conditional maximum principle. In addition, we include several specific examples, to highlight the importance of certain generic conditions, which are required in the statements of maximum principles of this type. Furthermore, we demonstrate how to obtain associated comparison theorems from our extended maximum principles.
Original languageEnglish
Article number20140079
JournalRoyal Society of London. Proceedings A. Mathematical, Physical and Engineering Sciences
Volume470
Issue number2167
Early online date7 May 2014
DOIs
Publication statusPublished - 8 Jul 2014

Keywords

  • Comparison theorems
  • Maximum principles
  • Parabolic partial differential equations

ASJC Scopus subject areas

  • Mathematics(all)
  • Engineering(all)
  • Physics and Astronomy(all)

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