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Kerr-Vaidya metrics are the simplest dynamical axially-symmetric solutions, all of which violate the null energy condition and thus are consistent with the formation of a trapped region in finite time according to distant observers. We…
We propose and analyze a space-time finite element method for Westervelt's quasilinear model of ultrasound waves in second-order formulation. The method combines conforming finite element spatial discretizations with a…
This paper introduces a new Windowed Green Function (WGF) method for the numerical integral-equation solution of problems of electromagnetic scattering by obstacles in presence of dielectric or conducting half-planes. The WGF method, which…
In this work, we have discretized a system of time-dependent nonlinear convection-diffusion-reaction equations with the virtual element method over the spatial domain and the Euler method for the temporal interval. For the nonlinear…
We study a bulk-surface coupled Laplace system involving an embedded open boundary. The problem is reformulated as an integro-differential equation using boundary integral representations, for which we establish existence and uniqueness of…
We develop embedding formulae for all possible diffraction problems with Dirichlet scatterers on square lattices using the Wiener--Hopf perspective. The embedding formula expresses solutions for arbitrary plane-wave incidence in terms of a…
Weyl gravity naturally generates effective dark matter and cosmological constant terms as integration constants, eliminating the need to explicitly introduce them into the theory. Additionally, the framework permits three intriguing…
In this paper, we propose a new numerical method for scattering problems in periodic waveguide, based on the newly established contour integral representation of solutions in a previous paper by the author (see [Zhadf]). For this kind of…
The methodology of the Riemann-Hilbert (RH) factorisation approach for Lax-pair isospectral deformations is used to derive, in the solitonless sector, the leading-order asymptotics as $t \to \pm \infty$ $(x/t \sim \mathcal{O}(1))$ of…
We derive the precise late-time asymptotics for solutions to the wave equation on extremal Reissner-Nordstr\"om black holes and explicitly express the leading-order coefficients in terms of the initial data. Our method is based on purely…
We address the problem of scattering and transmission of a plane flexural wave through a semi-infinite array of point scatterers/resonators, which take a variety of physically interesting forms. The mathematical model accounts for several…
In this paper, we consider the nonlinear doubly singular boundary value problems $(p(x)y'(x))'+ q(x)f(x,y(x))=0,~0<x<1$ with Dirichlet/Neumann boundary conditions at $x=0$ and Robin type boundary conditions at $x=1$. Due to the presence of…
Using the orbital-free density functional theory as a model theory, we present an analysis of the field theoretic approach to quasi-continuum method. In particular, by perturbation method and multiple scale analysis, we provide a formal…
In the present paper, it is provided a representation result for the weak solutions of a class of evolutionary Hamilton-Jacobi-Bellman equations on infinite horizon, with Hamiltonians measurable in time and fiber convex. Such Hamiltonians…
An interesting question is to characterize the general class of allowed boundary conditions for gauge theories, including gravity, at spatial and null infinity. This has played a role in discussions of soft charges, where antipodal symmetry…
It has recently been shown that the dynamics of perturbed non-rotating black holes (BHs) admits an infinite number of symmetries that are generated by the flow of the Korteweg-de Vries (KdV) equation. These symmetries lead to an infinite…
This article is concerned in establishing the existence and regularity of solution of semi-hyperbolic patch problem for two-dimensional isentropic Euler equations with van der Waals gas. This type of solution appears in the transonic flow…
We examine a new paradigm to account for the exponential decay seen in the light curves of some of the bright X-ray novae. These systems show an exponential decay in soft X-rays with an e-folding time constant of ~30 d. We investigate a…
A possible solution of the problem of time in the Wheeler - DeWitt quantum geometrodynamics is that time appears in semiclassical limit. Following this line of thinking, one can come to the Schrodinger equation for matter fields in curved…
Inspired by possibility that the Schwarzschild black hole may not be the unique spherically symmetric vacuum solution to generalisations of general relativity, we consider black holes in pure fourth order higher derivative gravity treated…