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Equivalence and symmetries of first order differential equations

V. Tryhuk (2008)

Czechoslovak Mathematical Journal

In this article, the equivalence and symmetries of underdetermined differential equations and differential equations with deviations of the first order are considered with respect to the pseudogroup of transformations x ¯ = ϕ ( x ) , y ¯ ...

Equivalence of ill-posed dynamical systems

Tomoharu Suda (2023)

Archivum Mathematicum

The problem of topological classification is fundamental in the study of dynamical systems. However, when we consider systems without well-posedness, it is unclear how to generalize the notion of equivalence. For example, when a system has trajectories distinguished only by parametrization, we cannot apply the usual definition of equivalence based on the phase space, which presupposes the uniqueness of trajectories. In this study, we formulate a notion of “topological equivalence” using the axiomatic...

Equivalent formulation and numerical analysis of a fire confinement problem

Alberto Bressan, Tao Wang (2010)

ESAIM: Control, Optimisation and Calculus of Variations

We consider a class of variational problems for differential inclusions, related to the control of wild fires. The area burned by the fire at time t> 0 is modelled as the reachable set for a differential inclusion x ˙ ∈F(x), starting from an initial set R0. To block the fire, a barrier can be constructed progressively in time. For each t> 0, the portion of the wall constructed within time t is described by a rectifiable set γ(t) ⊂ 2 . In this paper we show that the search for blocking strategies...

Equivariant degree of convex-valued maps applied to set-valued BVP

Zdzisław Dzedzej (2012)

Open Mathematics

An equivariant degree is defined for equivariant completely continuous multivalued vector fields with compact convex values. Then it is applied to obtain a result on existence of solutions to a second order BVP for differential inclusions carrying some symmetries.

Erweiterung des G -Stabilitätsbegriffes auf die Klasse der linearen Mehrschrittblockverfahren.

Reiner Vanselow (1983)

Aplikace matematiky

In der vorliegenden Arbeit wird der G -Stabilitätsbegriff von Dahlquist, der die Grundlage für Stabilitätsuntersuchungen bei linearen Mehrschrittverfahren zur Lösung nichtlinearet Anfangswertaufgaben bildet, auf die Klasse der linearen Mehrschrittblockverfahren übertragen. Es wird nachgewiesen, das Blockverfahren, die in diesem Sinne stabil sind, höchstens die Konsistenzordnung 2 haben können.

Estimates for Principal Lyapunov Exponents: A Survey

Janusz Mierczyński (2014)

Nonautonomous Dynamical Systems

This is a survey of known results on estimating the principal Lyapunov exponent of a timedependent linear differential equation possessing some monotonicity properties. Equations considered are mainly strongly cooperative systems of ordinary differential equations and parabolic partial differential equations of second order. The estimates are given either in terms of the principal (dominant) eigenvalue of some derived time-independent equation or in terms of the parameters of the equation itself....

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