Alexander V. Fominyh, Vladimir V. Karelin, Lyudmila N. Polyakova
Abstract:
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.
Submitted March 2, 2017. Published October 4, 2017.
Math Subject Classifications: 34A60, 49J52.
Key Words: Differential inequalities; Gateaux gradient; steepest descent method.
Show me the PDF file (177 KB), TEX file for this article.
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Alexander V, Fominyh Saint Petersburg State University 7-9, University emb. 199034 St. Petersburg, Russia email: alexfomster@mail.ru |
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Vladimir V. Karelin Saint Petersburg State University 7-9, University emb. 199034 St. Petersburg, Russia email: vlkarelin@mail.ru |
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Lyudmila N. Polyakova Saint Petersburg State University 7-9, University emb. 199034 St. Petersburg, Russia email: lnpol07@mail.ru |
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