A maximum principle for some nonlinear cooperative elliptic PDE systems with mixed boundary conditions

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Abstract

One of the classical maximum principles states that any nonnegative solution of a proper elliptic PDE attains its maximum on the boundary of a bounded domain. We suitably extend this principle to nonlinear cooperative elliptic systems with diagonally dominant coupling and with mixed boundary conditions. One of the consequences is a preservation of nonpositivity, i.e. if the coordinate functions or their fluxes are nonpositive on the Dirichlet or Neumann boundaries, respectively, then they are all nonpositive on the whole domain as well. Such a result essentially expresses that the studied PDE system is a qualitatively reliable model of the underlying real phenomena, such as proper reaction-diffusion systems in chemistry.

Original languageEnglish
Pages (from-to)900-910
Number of pages11
JournalJournal of Mathematical Analysis and Applications
Volume444
Issue number2
DOIs
Publication statusPublished - Dec 15 2016

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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