Application of the steepest descent method to solve differential inequalities

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In this article we consider the problem of finding the solution of a system of differential inequalities. We reduce the original problem to the unconstrained minimization of a functional. We find the Gateaux gradient for this functional, and then obtain nucessary and sufficient conditions for the existence of a minimum. Based on these conditions we apply the steepest descent method, and present a numerical implementation of the method.

Original languageEnglish
Article number241
Number of pages8
JournalElectronic Journal of Differential Equations
StatePublished - 4 Oct 2017

Scopus subject areas

  • Analysis


  • Differential inequalities
  • Gateaux gradient
  • Steepest descent metho


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