Monotone iterative technique for partial differential equations of first order
type: Item
instance of: scholarly article
title: Monotone iterative technique for partial differential equations of first order
zbMATH Open document ID: 0566.35016
DOI: 10.1016/0022-247X(84)90179-3
published in: Journal of Mathematical Analysis and Applications
publication date: 1984-01-01T00:00:00Z
review text: The authors are concerned with a monotone iterative technique for first- order partial differential equations of the form \(u_ t+\sum^{n}_{i=1}f_ i(t,x)u_{x_ i}=g(t,x,u),\) for \(0\leq t\leq T\) and \(a\leq x=(x_ 1,...,x_ n)\leq b\) \((a,b\in {\mathbb{R}}^ n)\). To this purpose they prove existence, uniqueness and comparison results. At last, an application to the construction of Lyapunov functions is given.
Mathematics Subject Classification ID: 35F20
Mathematics Subject Classification ID: 35A35
Mathematics Subject Classification ID: 35A05
Mathematics Subject Classification ID: 35B05
zbMATH DE Number: 3903125
zbMATH Keywords: monotone iterative technique
zbMATH Keywords: existence
zbMATH Keywords: uniqueness
zbMATH Keywords: comparison
zbMATH Keywords: Lyapunov functions
author: V. Lakshmikantham
author: M. Namik Oguztoereli
author: Aghalaya S. Vatsala
reviewed by: Gheorghe Moroşanu
MaRDI profile type: Publication
cites work: Q5330830
cites work: Q5569338
cites work: Stable and chaotic solutions of a first order partial differential equation
description: scientific article; zbMATH DE number 3903125