Partial differential analogs of ordinary differential equations and systems
type: Item
instance of: scholarly article
title: Partial differential analogs of ordinary differential equations and systems
zbMATH Open document ID: 1073.35182
author: Hakop Hakopian
author: Mariam G. Tonoyan
published in: The New York Journal of Mathematics
publication date: 2005-05-09T00:00:00Z
full work available at URL: https://eudml.org/doc/125186
full work available at URL: 10-6nf.htm
review text: The authors deal with the completely integrable overdetermined systems \[ \partial x/\partial x^i= f^i(x,z)\quad (x\in\mathbb{R}^n,\;z\in\mathbb{R}^m), \] where the solutions are ensured by the Frobenius theorem and then with the analogous higher-order generalizations with a single unknown function \((z\in\mathbb{R})\). The method of variation of constants, Wronskians, Liouville formula, fundamental set of solutions are introduced for the particular linear subcase. Explicit solutions for linear systems with constant coefficients are obtained. In other words, the authors simulate the well-known results for the ordinary differential equations \[ dz/dx= f(x,z),\quad x\in\mathbb{R},\quad z\in\mathbb{R}^m, \] or \[ d^nz/dx^n= f(x,z,\dots, d^{n-1} z/dx^{n-1}),\quad x,z\in \mathbb{R}, \] for the case of several independent variables.
reviewed by: Jan Chrastina
Mathematics Subject Classification ID: 35N05
Mathematics Subject Classification ID: 35F20
Mathematics Subject Classification ID: 58A17
zbMATH DE Number: 2166316
zbMATH Keywords: Frobenius theorem
zbMATH Keywords: Wronskian
zbMATH Keywords: variation of constants
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 2166316