Detail publikace

Compatible and incompatible nonuniqueness conditions for the classical Cauchy problem

Originální název

Compatible and incompatible nonuniqueness conditions for the classical Cauchy problem

Anglický název

Compatible and incompatible nonuniqueness conditions for the classical Cauchy problem

Jazyk

en

Originální abstrakt

In the first part of this paper sufficient conditions for nonuniqueness of the classical Cauchy problem $\dot{x}=f(t,x)$, $x(t_0)=x_0$ are given. As the essential tool serves a method which estimates the distance'' between two solutions with an appropriate Lyapunov function and permits to show that under certain conditions the distance'' between two different solutions vanishes at the initial point. In the second part attention is paid to conditions that are obtained by a formal inversion of uniqueness theorems of Kamke-type but cannot guarantee nonuniqueness because they are incompatible.

Anglický abstrakt

In the first part of this paper sufficient conditions for nonuniqueness of the classical Cauchy problem $\dot{x}=f(t,x)$, $x(t_0)=x_0$ are given. As the essential tool serves a method which estimates the distance'' between two solutions with an appropriate Lyapunov function and permits to show that under certain conditions the distance'' between two different solutions vanishes at the initial point. In the second part attention is paid to conditions that are obtained by a formal inversion of uniqueness theorems of Kamke-type but cannot guarantee nonuniqueness because they are incompatible.

BibTex


@article{BUT72872,
author="Josef {Diblík} and Christine {Nowak}",
title="Compatible and incompatible nonuniqueness conditions for the classical Cauchy problem",
annote="In the first part of this paper sufficient conditions for nonuniqueness of the classical Cauchy problem
$\dot{x}=f(t,x)$, $x(t_0)=x_0$
are given. As the essential tool serves a method which estimates
the distance'' between two solutions with an appropriate Lyapunov function
and permits to show that under certain conditions the distance'' between two different solutions
vanishes at the initial point. In the second part attention is paid to
conditions that are obtained by a formal inversion of uniqueness theorems of
Kamke-type but cannot guarantee nonuniqueness because they are
incompatible.",
chapter="72872",
number="1",
volume="2011",
year="2011",
month="august",
pages="1--15",
type="journal article - other"
}