Related papers: Unpredictable Solutions of Linear Differential Equ…
When high-dimensional non-uniformly hyperbolic chaotic systems undergo dynamical perturbations, their long-time statistics are generally observed to respond differentiably with respect to the perturbation. Although important in…
In this paper we study the construction of a discrete solution for a hyperbolic system of partial differentials of the strongly coupled type. In its construction, the discrete separation of matricial variable method was followed. Two…
In the first part of this article, we will prove an existence-uniqueness result for generalized solutions of a mixed problem for linear hyperbolic system in the Colombeau algebra. In the second part, we apply this result to a wave…
Properties of solutions of generic hyperbolic systems with multiple characteristics with diagonalizable principal part are investigated. Solutions are represented as a Picard series with terms in the form of iterated Fourier integral…
We consider generic differential equations in $\mathbb{R}$ with a finite number of hyperbolic equilibria, which are subject to $\omega$--periodic instantaneous perturbative pulses ($\omega>0$). Using the time-$ \omega$ map of the original…
We study existence and uniqueness of solutions to a class of nonlinear degenerate parabolic equations, in bounded domains. We show that there exists a unique solution which satisfies possibly inhomogeneous Dirichlet boundary conditions. To…
An elementary example shows that the number of zeroes of a component of a solution of a system of linear ordinary differential equations cannot be estimated through the norm of coefficients of the system alone.
The goal of this work is to determine classes of traveling solitary wave solutions for Lattice Boltzmann schemes by means of an hyperbolic ansatz. It is shown that spurious solitary waves can occur in finite-difference solutions of…
We consider the stability of a system of equations which are a singular perturbation of the incompressible rigid-plastic flow equations used to model granular flow. A linear stability analysis shows that solutions of these equations are…
We consider the Cauchy problem for a system of fully nonlinear parabolic equations. In this paper, we shall show the existence of global-in-time solutions to the problem. Our condition to ensure the global existence is specific to the fully…
We consider a non-linear stochastic wave equation driven by space-time white noise in dimension 1. First of all, we state some results about the intermittency of the solution, which have only been carefully studied in some particular cases…
We study inhomogeneous non-strictly hyperbolic systems of two equations, which are a formal generalization of the transformed one-dimensional Euler-Poisson equations. For such systems, a complete classification of the behavior of the…
In this paper, we consider nonlinearly perturbed Legendre differential equations subject to the usual boundary conditions. For such problems we establish sufficient conditions for the existence of solutions and in some cases we provide a…
We present a computational analysis of a 2$\times$2 hyperbolic system of balance laws whose solutions exhibit complex nonlinear behavior. Traveling-wave solutions of the system are shown to undergo a series of bifurcations as a parameter in…
A bosonized nonlinear (polynomial) supersymmetry is revealed as a hidden symmetry of the finite-gap Lame equation. This gives a natural explanation for peculiar properties of the periodic quantum system underlying diverse models and…
In this article we study a class of generalised linear systems of difference equations with given non-consistent initial conditions and infinite many solutions. We take into consideration the case that the coefficients are square constant…
We consider time-independent solutions of hyperbolic equations such as $\d_{tt}u -\Delta u= f(x,u)$ where $f$ is convex in $u$. We prove that linear instability with a positive eigenfunction implies nonlinear instability. In some cases the…
In this paper, we study the existence and non-existence of entire solutions of certain non-linear delay-differential equations.
We systematically introduce the idea of applying differential operator method to find a particular solution of an ordinary nonhomogeneous linear differential equation with constant coefficients when the nonhomogeneous term is a polynomial…
In this article we show the existence of a random-field solution to linear stochastic partial differential equations whose partial differential operator is hyperbolic and has variable coefficients that may depend on the temporal and spatial…