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
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...
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 ∈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) ⊂. In this paper we show that the search for blocking strategies...
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.
In der vorliegenden Arbeit wird der -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.
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....
A theorem on estimates of solutions of impulsive parabolic equations by means of solutions of impulsive ordinary differential equations is proved. An application to the population dynamics is given.