I. L. Kogan, “Method of Duhamel Integral for Ordinary Differential Equations with Constant Coefficients in Respect to the Theory of Distributions”, Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 2010, Issue 1(20),Pages <nobr>37

This article is cited in 5 papers

Differential Equations

Method of Duhamel Integral for Ordinary Differential Equations with Constant Coefficients in Respect to the Theory of Distributions

I. L. Kogan

Dept. of Higher Mathematics, Russian State Agrarian University – Moscow Agricultural Academy after K. A. Timiryazev, Moscow

Abstract: A new proof for the method of Duhamel integral is produced. This proof is based on the convolution algebra of distributions and allows to extend this method for the region $x<0$. Universal formulas for solving equations with discontinuos right-hand side are obtained.

Keywords: Duhamel integral, space of distributions, convolution of distributions, convolution of distributions, convolution algebra.

UDC: 517.926+517.982.45

MSC: 34L40, 47E05

Original article submitted 05/II/2009
revision submitted – 01/IX/2009

DOI: 10.14498/vsgtu673