Related papers: Explicit representation of solutions to a linear w…

The classic problem of the dynamic evolution of Langmuir electron waves in a collisionless plasma and their Landau damping is cast as a second-order, self-adjoint problem with a continuum spectrum of real and positive squared frequencies.…

We show that if a solution to the water wave equation, for an arbitrary short time interval, is flat on an open set and the horizontal fluid velocity at the surface is zero on the same open set, then the wave must vanish everywhere for all…

We study the existence of a periodic solution for a differential equation with distributed delay. It is shown that, for a class of distributed delay diferential quations, a symmetric period 2 solution, where the period is twice the maximum…

Using nonstandard methods, we show that the time dependent Fourier series of any smooth function F, solving the wave equation, on a finite closed interval, with vanishing boundary conditions, converges uniformly to F.

The goal of the present work is to solve a linear dispersive equation with variable coefficient advection on an unbounded domain. In this setting, transparent boundary conditions are vital to allow waves to leave (or even re-enter) the,…

Time-delay dynamical systems inherently embody infinite-dimensional dynamics, thereby amplifying their complexity. This aspect is especially notable in nonlinear dynamical systems, which frequently defy analytical solutions and necessitate…

The paper continues the analysis, started in [1] (Part I,arXiv:2302.04353), of the model open wave-guide problem defined by 2 semi-infinite, rectangular wave-guides meeting along a common perpendicular line. In Part I we reduce the solution…

This paper explores the exponential stability of two nonlinear wave equations coupled through their velocities. The analysis is divided into two main cases. First, we consider a system where one equation is damped, while the other…

Ordinary differential equations of the second order with one constant delay are considered in this paper. An analytical representation of the solution is obtained using the method of steps.

A recent line of work in the machine learning community addresses the problem of predicting high-dimensional spatiotemporal phenomena by leveraging specific tools from the differential equations theory. Following this direction, we propose…

A high-frequency recovered fully discrete low-regularity integrator is constructed to approximate rough and possibly discontinuous solutions of the semilinear wave equation. The proposed method, with high-frequency recovery techniques, can…

We show how the recent extension of spectral submanifold (SSM) theory to delay differential equations (DDEs) enables data-driven model reduction of nonlinear delay systems. First, using a scalar DDE with a single discrete delay, we compare…

In this paper, the use of partitioned linear multistep methods (PLMM) as time integrators for the numerical approximation of some partial differential equations (pdes) is studied. We consider the periodic initial-value problem of two…

In this paper we will consider the peridynamic equation of motion which is described by a second order in time partial integro-differential equation. This equation has recently received great attention in several fields of Engineering…

We study stochastic delay differential equations (SDDE) where the coefficients depend on the moving averages of the state process. As a first contribution, we provide sufficient conditions under which a linear path functional of the…

The nonlinear hyperbolic system of pde's governing the evolution of the deformation of isotropic hyperelastic materials is considered. In the absence of boundaries and with an additional nonresonance or null condition, the system has global…

A one-way wave equation is an evolution equation in one of the space directions that describes (approximately) a wave field. The exact wave field is approximated in a high frequency, microlocal sense. Here we derive the pseudodifferential…

We investigate the evolution of dispersive waves governed by linear wave equations, where a finite duration source is applied. The resulting wave may be viewed as the superposition of modes before the source is turned on and after it is…

We numerically evolve spherically symmetric solutions to the linear wave equation on some expanding Friedmann-Lema\^itre-Robertson-Walker (FLRW) spacetimes and study the respective asymptotics for large times. We find a quantitative…

This paper focuses on explicit approximations for nonlinear stochastic delay differential equations (SDDEs). Under the weakly local Lipschitz and some suitable conditions, a generic truncated Euler-Maruyama (TEM) scheme for SDDEs is…