Related papers: Wave equations on silent big bang backgrounds
We find the shock wave solutions in a class of cosmological backgrounds with a null singularity, each of these backgrounds admits a matrix description. A shock wave solution breaks all supersymmetry meanwhile indicates that the interaction…
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…
By definition, the exterior asymptotic energy of a solution to a wave equation on $\mathbb{R}^{1+N}$ is the sum of the limits as $t\to \pm\infty$ of the energy in the the exterior $\{|x|>|t|\}$ of the wave cone. In our previous work (JEMS…
Two-dimensional free-surface flow over localised topography is examined with the emphasis on the stability of hydraulic-fall solutions. A Gaussian topography profile is assumed with a positive or negative amplitude modelling a bump or a…
This article concerns the long term behavior of solutions to a structural acoustic model consisting of a semilinear wave equation defined on a smooth bounded domain $\Omega\subset\mathbb{R}^3$ which is coupled with a Berger plate equation…
We derive a new formulation of the compressible Euler equations exhibiting remarkable structures, including surprisingly good null structures. The new formulation comprises covariant wave equations for the Cartesian components of the…
We consider a class of wave equations with constant damping and polynomial nonlinearities that are perturbed by small, multiplicative, space-time white noise. The equations are defined on a one-dimensional bounded interval with Dirichlet…
Systems of wave equations may fail to be globally well posed, even for small initial data. Attempts to classify systems into well and ill-posed categories work by identifying structural properties of the equations that can work as…
Two classes of stationary axisymmetric solutions of Einstein's equations for isolated differentially rotating matter sources are presented. The asymptotic regime is extracted, with attention to quasilocal gravitational energy, shear and…
$\sigma_k$-Yamabe equations are conformally invariant equations generalizing the classical Yamabe equation. In an earlier work YanYan Li proved that an admissible solution with an isolated singularity at $0\in \mathbb R^n$ to the…
For the damped wave equation on the torus, when some geodesics never meet the positive set of the damping, energy decay rates are known to depend on derivative bounds and growth properties of the damping near the boundary of its support, as…
We study a nonlocal wave equation with logarithmic damping which is rather weak in the low frequency zone as compared with frequently studied strong damping case. We consider the Cauchy problem for this model in the whole space and we study…
We study the problem of estimating the coefficients in linear ordinary differential equations (ODE's) with a diverging number of variables when the solutions are observed with noise. The solution trajectories are first smoothed with local…
We derive the asymptotic traveling-wave solutions of the nonlinear 1-dimensional Balitsky-Kovchegov QCD equation for rapidity evolution in momentum-space, with 1-loop running coupling constant and equipped with the…
This paper is concerned with the global stability of the plane wave solutions to the relativistic string equation with non-small perturbations. Under certain decay assumptions on the plane wave, we conclude that the perturbed system admits…
Coupled wave equations are popular tool for investigating longitudinal dynamical effects in semiconductor lasers, for example, sensitivity to delayed optical feedback. We study a model that consists of a hyperbolic linear system of partial…
An asymptotic theory is developed for computing volumes of regions in the parameter space of a directed Gaussian graphical model that are obtained by bounding partial correlations. We study these volumes using the method of real log…
In this paper, we study the asymptotic behavior of solutions to the wave equation with damping depending on the space variable and growing at the spatial infinity. We prove that the solution is approximated by that of the corresponding heat…
Analytical and numerical methods are developed to analyze the quantum nature of the big bang in the setting of loop quantum cosmology. They enable one to explore the effects of quantum geometry both on the gravitational and matter sectors…
Asymptotic behavior of a class of nonlinear Schr\"odinger equations are studied. Particular cases of 1D weakly focusing and Bose-Einstein condensates are considered. A statistical approach is presented to describe the stationary probability…