相关论文: Shadowing matching errors for wave-front-like solu…

This article is the first of two in which we develop a geometric framework for analysing silent and anisotropic big bang singularities. The results of the present article concern the asymptotic behaviour of solutions to linear systems of…

For the nonlinear wave equation $u_{tt} - c(u)\big(c(u) u_x\big)_x~=~0$, it is well known that solutions can develop singularities in finite time. For an open dense set of initial data, the present paper provides a detailed asymptotic…

An averaging method for getting uniformly valid asymptotic approximations of the solution of hyperbolic systems of equations is presented. The averaged system of equations disintegrates into independent equations for non-resonance systems.…

This article examines the accuracy for large times of asymptotic expansions from periodic homogenization of wave equations. As usual, $\epsilon$ denotes the small period of the coefficients in the wave equation. We first prove that the…

Solutions to the stochastic wave equation on the unit sphere are approximated by spectral methods. Strong, weak, and almost sure convergence rates for the proposed numerical schemes are provided and shown to depend only on the smoothness of…

Single-view point cloud completion aims to recover the full geometry of an object based on only limited observation, which is extremely hard due to the data sparsity and occlusion. The core challenge is to generate plausible geometries to…

In this paper, we present and analyze an energy-conserving and linearly implicit scheme for solving the nonlinear wave equations. Optimal error estimates in time and superconvergent error estimates in space are established without time-step…

This is the full and extended version of the brief note arXiv:1908.00938. A nontrivially solvable 4-dimensional Hamiltonian system is applied to the problem of wave fronts and to the asymptotic theory of partial differential equations. The…

This paper explores backward error analysis for numerical solutions of ordinary differential equations, particularly focusing on chaotic systems. Three approaches are examined: residual assessment, the method of modified equations, and…

The paper explores the Rutherford scattering shadow in an entire class of comoving frames -- inertial frames moving along the initial projectile direction -- of which the laboratory frame, where the target is initially at rest, is a…

Thick biological tissues give rise to not only the scattering of incoming light waves, but also aberrations of the remaining unscattered waves. Due to the inability of existing optical imaging methodologies to overcome both of these…

This paper investigates the scattering of biharmonic waves by a one-dimensional periodic array of cavities embedded in an infinite elastic thin plate. The transparent boundary conditions are introduced to formulate the problem from an…

In this work, an efficient approximation scheme has been proposed for getting accurate approximate solution of nonlinear partial differential equations with constant or variable coefficients satisfying initial conditions in a series of…

Formulas are derived for solutions of many-body wave scattering problems by small particles in the case of acoustically soft, hard, and impedance particles embedded in an inhomogeneous medium. The limiting case is considered, when the size…

We consider time-harmonic electromagnetic wave equations in composites of a dispersive material surrounded by a classical material. In certain frequency ranges this leads to sign-changing permittivity and/or permeability. Previously meshing…

The behavior of a class of solutions of the shallow water Airy system originating from initial data with discontinuous derivatives is considered. Initial data are obtained by splicing together self-similar parabolae with a constant…

We are interested in nonlinear hyperbolic systems in nonconservative form arising in fluid dynamics, and, for solutions containing shock waves, we investigate the convergence of finite difference schemes applied to such systems. According…

The study of spherically symmetric motion is important for the theory of explosion waves. In this paper, we construct rigorously self-similar solutions to the Riemann problem of the spherically symmetric Euler equations for general…

We study the problem of identifying the parameters of a linear system from its response to multiple unknown waveforms. We assume that the system response is a scaled superposition of time-delayed and frequency-shifted versions of the…

We deal with the singularly perturbed Nagumo-type equation $$ \epsilon^2 u'' + u(1-u)(u-a(s)) = 0, $$ where $\epsilon > 0$ is a real parameter and $a: \mathbb{R} \to \mathbb{R}$ is a piecewise constant function satisfying $0 < a(s) < 1$ for…