Quasi-flows and equations with nonlinear differentials
type: Item
instance of: scholarly article
title: Quasi-flows and equations with nonlinear differentials
zbMATH Open document ID: 1017.34004
DOI: 10.1016/S0362-546X(01)00883-5
author: Peter E. Kloeden
author: I. E. Vasilyeva
author: B. N. Sadovskiĭ
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2002-11-28T00:00:00Z
review text: The authors introduce an equation with a nonlinear differential \[ \phi (t+dt)-\phi (t)-D_{t,\phi (t)}(dt)=o(dt),\tag{*} \] where the mapping \(D_{t,x}: \mathbb R^{+}\rightarrow\mathbb R^d\) is defined for suitable \((t,x)\in\mathbb R\times\mathbb R^d\). The initial value problem for (*) is to find a function \(\phi\) satisfying (*) and the initial condition \(\phi(t_0)=x_0\). A local existence and uniqueness theorem on the problem is proved. The motivations come from applied problems that involve nonsmooth evolution processes satisfying the evolution properties, but which are not solutions to a classical differential equation.
Mathematics Subject Classification ID: 34A12
Mathematics Subject Classification ID: 34A34
Mathematics Subject Classification ID: 34C99
Mathematics Subject Classification ID: 37C99
zbMATH DE Number: 1836636
zbMATH Keywords: quasi-flows
zbMATH Keywords: quasi-differential equations
reviewed by: Klaudiusz Wójcik
MaRDI profile type: Publication
cites work: Q3324260
cites work: Q5665783
cites work: Q5513216
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full work available at URL: s0362-546x(01)00883-5
OpenAlex ID: W2071247787
description: scientific article; zbMATH DE number 1836636