Existence and asymptotic behaviour for a discrete hyperbolic system

Existence for a Class of Discrete Hyperbolic Problems

Existence and Uniqueness for a Variational Hyperbolic System without Resonance

Existence and Asymptotic Stability of Solutions for Hyperbolic Differential Inclusions with a Source Term

Existence and asymptotic stability of relaxation discrete shock profiles

In this paper we study the asymptotic nonlinear stability of discrete shocks of the relaxing scheme for approximating the general system of nonlinear hyperbolic conservation laws. The existence of discrete shocks is established by suitable manifold construction, and it is shown that weak single discrete shocks for such a scheme are nonlinearly stable in L2, provided that the sums of the initial...

Asymptotic Behaviour of a Discrete Dynamical System Generated by a Simple Evolutionary Process

A simple model of phenotypic evolution is introduced and analysed in a space of population states. The expected values of the population states generate a discrete dynamical system. The asymptotic behaviour of the system is studied with the use of classical tools of dynamical systems. The number, location and stability of fixed points of the system depend on parameters of a fitness function and...