We study the pointwise behavior of perturbations from a viscous shock solution to a scalar conservation law, obtaining an estimate independent of shock strength. We find that for a perturbation with initial data decaying algebraically or slower, the perturbation decays in time at the rate of decay of the integrated initial data in any Lp norm, p ≥ 1. Stability in any Lp norm is a direct consequ...

The Boltzmann equation for a gas of smooth, inelastic hard spheres is introduced and its homogeneous solution for an isolated system is discussed. The possibility of hydrodynamic excitations is explored using the linearized Boltzmann equation for small spatial perturbations of the homogeneous state. It is shown that the spectrum of the generator for this linear dynamics contains five points at ...

We study scalar perturbations to a Robertson-Walker cosmological metric in terms of a pseudo-Newtonian potential, which emerges naturally from the solution of the field equations. This potential is given in terms of a Green function for matter density fluctuations of arbitrary amplitude whose time and spatial dependence are assumed known. The results obtained span both the linearized and Newton...

A modification of the parabolic Allen–Cahn equation, determined by the substitution of Fick’s diffusion law with a relaxation relation of Cattaneo-Maxwell type, is considered. The analysis concentrates on traveling fronts connecting the two stable states of the model, investigating both the aspects of existence and stability. The main contribution is the proof of the nonlinear stability of the ...

Abstract: This paper presents a delay-dependent robust stochastic active queue management (AQM) scheme that can be implemented in the routers for stabilizing queues in transmission control protocol (TCP) communication networks. The linearized TCP/AQM system is modelled as a uncertain time-delay system with stochastic perturbations and time-varying network parameters. In this paper, a new flow m...

Models with vector fields acquiring a nonvanishing vacuum expectation value along one spatial direction have been proposed to sustain a prolonged stage of anisotropic accelerated expansion. Such models have been used for realizations of early time inflation, with a possible relation to the large scale cosmic microwave background anomalies, or of the late time dark energy. We show that, quite ge...

We review the WKB method for multicomponent fields obeying hyperbolic linear partial differential equations and derive a general necessary and sufficient condition for the formalism to provide transport equations. We apply the method to linearized perturbations of perfect fluid solutions to Einstein’s equation and show that the gravitational and sound wave modes satisfy this condition, whereas ...

This paper uses the assumptions of ergodicity and a microcanonical distribution to compute estimates of the largest Lyapunov exponents in lower-dimensional Hamiltonian systems. That the resulting estimates are in reasonable agreement with the actual values computed numerically corroborates the intuition that chaos in such systems can be understood as arising generically from a parametric instab...

We study scalar perturbations to a Robertson-Walker cosmological metric in terms of a pseudo-Newtonian potential, which emerges naturally from the solution of the field equations. This potential is given in terms of a Green function for matter density fluctuations of arbitrary amplitude whose time and spatial dependence are assumed known. The results obtained span both the linearized and Newton...

In this paper we give a complete description of the Fredholm spectrum of the linearized 3D Euler equation in terms of the dynamical spectrum of the cocycle governing the evolution of shortwave perturbations. The argument is based on the pseudo differential representation of the Euler group and an application of an abstract isomorphism theorem for operator C∗-algebras. We further show that for a...