Related papers: The Helically-Reduced Wave Equation as a Symmetric…
A relativistic equation is proposed for the bound state of two particles, which is in accord with the boundary condition for the propagation of the negative-energy states and reduces to the (one-body)Dirac equation in the infinite limit of…
We consider an elliptic pseudo differential equation in a multi-dimensional cone and starting wave factorization concept we add some boundary conditions. For the simplest cases explicit formulas for solution are given like layer potentials…
We consider the problem \begin{equation}(1)\;\;\; \begin{cases} S_k(D^2u)= \lambda |x|^{\sigma} (1-u)^q &\mbox{in }\;\; B,\\ u <0 & \mbox{in }\;\; B,\\ u=0 &\mbox{on }\partial B, \end{cases} \end{equation} where $B$ denotes the unit ball in…
We show that for an eikonal limit of gravity in a space-time of any dimension with a non-vanishing cosmological constant, the Einstein -- Hilbert action reduces to a boundary action. This boundary action describes the interaction of…
A new class of linear second order hyperbolic partial differential operators satisfying Huygens' principle in Minkowski spaces is presented. The construction reveals a direct connection between Huygens' principle and the theory of solitary…
We investigate bound states of a non-relativistic scalar particle in a three-dimensional helically twisted (torsional) geometry, considering both the free case and the presence of external radial interactions. The dynamics is described by…
Photonic computing has recently become an interesting paradigm for high-speed calculation of computing processes using light-matter interactions. Here, we propose and study an electromagnetic wave-based structure with the ability to…
By careful exploration of separation of variables into the Laplacian in spherical coordinates, we obtain the extra delta-like singularity, elimination of which restricts the radial wave function at the origin. This constraint has the form…
A new analytical formulation is prescribed to solve the Helmholtz equation in 2D with arbitrary boundary. A suitable diffeomorphism is used to annul the asymmetries in the boundary by mapping it into an equivalent circle. This results in a…
In the present paper, we study the Dirac equation in the background of Minkowski space-time on a light cone. With the help of the coupling of the radial parts, the system of 4 equations is reduced to two different second-order differential…
We consider the convected Helmholtz equation with a generalized Myers boundary condition (a boundary condition of the second-order) and characterize the set of physical parameters for which the problem is weakly well-posed. The model comes…
This paper treats the time-harmonic electro-magnetic scattering or radiation problem governed by Maxwell's equations in an exterior weak Lipschitz domain divided into two disjoint weak Lipschitz parts We will present a solution theory using…
We consider the identification of a nonlinear friction law in a one-dimensional damped wave equation from additional boundary measurements. Well-posedness of the governing semilinear hyperbolic system is established via semigroup theory and…
It was shown recently that the constraints on the initial data for Einstein's equations may be posed as an evolutionary problem [9]. In one of the proposed two methods the constraints can be replaced by a first order symmetrizable…
A relativistic equation is deduced for the bound state of two particles, by assuming a proper boundary condition for the propagation of the negative-energy states. It reduces to the (one-body)Dirac equation in the infinite limit of one of…
This paper proposes a volumetric penalty method to simulate the boundary conditions for a non-linear hyperbolic problem. The boundary conditions are assumed to be maximally strictly dissipative on a non-characteristic boundary. This…
For spherically symmetric repulsive Hamiltonians we prove the Besov bound, the radiation condition bounds and the limiting absorption principle. The Sommerfeld uniqueness result also follows as a corollary of these. In particular, the…
We investigate the well-posedness of a class of stochastic second-order in time damped evolution equations in Hilbert spaces, subject to the constraint that the solution lie within the unitary sphere. Then, we focus on a specific example,…
We present a dissipative algorithm for solving nonlinear wave-like equations when the initial data is specified on characteristic surfaces. The dissipative properties built in this algorithm make it particularly useful when studying the…
We study conditions of reduction of the multidimensional wave equation - a system of the d'Alembert and Hamilton equations. We prove necessary conditions for compatibility of such system of the reduction conditions. Possible types of the…