Related papers: A Note on Wave Equation in Einstein & de Sitter Sp…
We reexamine the general solution of a Schr\"{o}dinger equation in the presence of a time-dependent linear potential in configuration space based on the Lewis-Riesenfeld framework. For comparison, we also solve the problem in momentum space…
The Liouville-von Neumann equation describes the change in the density matrix with time. Interestingly, this equation was recently regarded as a wave equation for wave functions but not a equation for density functions. This setting leads…
In this work, we are concerned with a nonlinear wave equation with variable exponents. A distributive delay is imposed into the damping term with variable exponents nonlinearity. Firstly, we show that the global nonexistence time can be…
We present a covariant study of static space-times, as such and as solutions of gravity theories. By expressing the relevant tensors through the velocity and the acceleration vectors that characterise static space-times, the field equations…
In recent time, by working in a plane with the metric associated with wave equation (the Special Relativity non-definite quadratic form), a complete formalization of space-time trigonometry and a Cauchy-like integral formula have been…
In this article, we study a direct and an inverse problem for the bi-wave operator $(\Box^2)$ along with second and lower order time-dependent perturbations. In the direct problem, we prove that the operator is well-posed, given initial and…
The classical relativistic wave equations are presented as partial difference equations in the arena of covariant discrete phase space. These equations are also expressed as difference-differential equations in discrete phase space and…
In this article we shall go over recent work in proving dispersive and Strichartz estimates for the Dirichlet-wave equation. We shall discuss applications to existence questions outside of obstacles and discuss open problems.
We examine the solutions of the semilinear wave equation, and, in particular, of the $\varphi ^p$ model of quantum field theory in the curved space-time. More exactly, for $1< p<4$ we prove that solution of the massless self-interacting…
This paper is concerned with the asymptotic behavior of the solution to the Euler equations with time-depending damping on quadrant $(x,t)\in \mathbb{R}^+\times\mathbb{R}^+$, \begin{equation}\notag \partial_t v - \partial_x u=0, \qquad…
The computational analysis of the Cauchy problem for semi-linear Klein-Gordon equations in the de Sitter spacetime is considered. Several simulations are performed to show the time-global behaviors of the solutions of the equations in the…
We solve the source free electromagnetic wave equation in Friedmann-Robertson-Walker space-times for curvature $K=0$ and $K=-1$. Deriving a solution expression in the form of spherical means we deduce and compare two properties of the…
This paper deals with the long time behavior of solutions to a "fractional Fokker-Planck" equation of the form $\partial_t f = I[f] + \text{div}(xf)$ where the operator $I$ stands for a fractional Laplacian. We prove an exponential in time…
In this paper, we are concerned with the stochastic time-fractional diffusion-wave equations in a Hilbert space. The main objective of this paper is to establish properties of the stochastic weak solutions of the initial-boundary value…
In this paper we study the classical Hilbert space introduced by Koopman and von Neumann in their operatorial formulation of classical mechanics. In particular we show that the states of this Hilbert space do not spread, differently than…
We consider wave models with lower order terms and recollect some recent results on energy and dispersive estimates for their solution based on symbolic type estimates for coefficients and partly stabilisation conditions. The exposition is…
In this work we present a deformed model of Einstein-Proca space-time based on the replacement of point-like sources by non-commutative smeared distributions. We discuss the solutions to the set of non-commutative Einstein-Proca equations…
We interpret, in the realm of relativistic quantum field theory, the tangential operator given by Coleman, Mandula as an appropriate coordinate operator. The investigation shows that the operator generates a Snyder-like noncommutative…
The Maxwell equations for the electromagnetic potential, supplemented by the Lorenz gauge condition, are decoupled and solved exactly in de Sitter space-time studied in static spherical coordinates. There is no source besides the…
In this paper we construct negatively curved Einstein spaces describing gravitational waves having a solvegeometry wave-front (i.e., the wave-fronts are solvable Lie groups equipped with a left-invariant metric). Using the Einstein…