Electronic Journal of Differential Equations (Oct 2017)

Application of the steepest descent method to solve differential inequalities

  • Alexander V. Fominyh,
  • Vladimir V. Karelin,
  • Lyudmila N. Polyakova

Journal volume & issue
Vol. 2017, no. 241,
pp. 1 – 8

Abstract

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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.

Keywords