Related papers: Equivalence of energy methods in stability theory
We consider nonholonomic systems with nonlinear restrictions with respect to the velocities. The mathematical problem is formulated by means of the Voronec equations extended to the nonlinear case. The main point of the paper is the balance…
The stability of a special class of equilibria for the free rigid body on $\mathfrak{so}(5)$ is discussed. An instability region and two stability regions are established. The list of constants of motion which assure the complete…
Although stable solutions of dynamical systems are typically considered more important than unstable ones, unstable solutions have a critical role in the dynamical integrity of stable solutions. In fact, usually, basins of attraction…
In this paper we consider some stabilization problems for the wave equation with switching. We prove exponential stability results for appropriate damping coefficients. The proof of the main results is based on D'Alembert formula and some…
We show that for continuous time dynamical systems described by polynomial differential equations of modest degree (typically equal to three), the following decision problems which arise in numerous areas of systems and control theory…
We consider the periodic problem for two-fluid non-isentropic Euler-Maxwell systems in plasmas. By means of suitable choices of symmetrizers and an induction argument on the order of the time-space derivatives of solutions in energy…
It is shown that the total energy of the static "field + particle" system, defined in the framework of classical, renormalized electrodynamics of particles and fields, depends in an unstable way upon the field boundary data. It is argued…
The kinetic energy is estimated for the ground-state of liquid $^3$He at equilibrium density. The obtained value for this quantity, $10.16\pm0.05$ K/atom at density $0.0163~\mbox{\AA}$, is in agreement with most of the experimental data…
We investigate stability of a solution of a hybrid system in the sense that the graphs of solutions from nearby initial conditions remain close and tend towards the graph of the given solution. In this manner, a small continuous-time…
The basic elements of the mathematical theory of states of thermal equilibrium of infinite systems of quantum anharmonic oscillators (quantum crystals) are outlined. The main concept of this theory is to describe the states of finite…
This paper synthesizes anytime algorithms, in the form of continuous-time dynamical systems, to solve monotone variational inequalities. We introduce three algorithms that solve this problem: the projected monotone flow, the safe monotone…
The stability conditions of a relativistic hydrodynamic theory can be derived directly from the requirement that the entropy should be maximised in equilibrium. Here we use a simple geometrical argument to prove that, if the hydrodynamic…
We say that an algorithm is stable if small changes in the input result in small changes in the output. This kind of algorithm stability is particularly relevant when analyzing and visualizing time-varying data. Stability in general plays…
Spectral methods, thanks to the high accuracy and the possibility to use fast algorithms, represent an effective way to approximate the Boltzmann collision operator. On the other hand, the loss of some local invariants leads to the wrong…
The main topic of this work concerns the formulation of the equations of motion and the consequent energy balance that they imply for this type of systems, In particular, the analytical development that we will carry out on the equations of…
This paper provides two results that are useful in the study of the existence and the stability properties of a periodic solution for a given dynamical system. The first result deals with scalar time-periodic systems and establishes the…
Consistency and stability are two essential ingredients in the design of numerical algorithms for partial differential equations. Robust algorithms can be developed by incorporating nonlinear physical stability principles in their design,…
The main purpose of this paper is to present a general method for the controllability of the stability of a system of fractional-order differential equations around its equilibrium states. This method is applied to analyze and control the…
The concept of efficiency plays a prominent role in the formal solution of decision problems that involve incomparable alternatives. This paper develops necessary and sufficient conditions for the efficient points in a sum of sets of…
We characterize stability under composition, inversion, and solution of ordinary differential equations for ultradifferentiable classes, and prove that all these stability properties are equivalent.