Related papers: Analytical solution to the Langmuir spherical prob…
The boundary-value problem for the perturbation of an electric potential by a homogeneous anisotropic dielectric sphere in vacuum was formulated. The total potential in the exterior region was expanded in series of radial polynomials and…
We consider the total energy decay of the Cauchy problem for wave equations with a potential and an effective damping. We treat it in the whole one-dimensional Euclidean space. Fast energy decay is established with the help of potential.…
The Rayleigh equation for bubble dynamics is widely used. However, analytical solutions of this equation have not been obtained previously. Here we find closed--form general solutions of the Rayleigh equation both for an empty and…
We obtain exact solutions to the class of parabolic partial differential equations of arbitrary dimensionality and with arbitrary potentials. The solutions are presented in a compact-form: as explicit mathematical expressions consisting of…
We consider the Cauchy problem with smooth and compactly supported initial data for the wave equation in a general class of spherically symmetric geometries which are globally smooth and asymptotically flat. Under certain mild conditions on…
A general solution to linearized Vlasov equation for an electron electrostatic wave in a homogeneous unmagnetized plasma is derived. The quasi-linear diffusion coefficient resulting from this solution is a continuous function of omega in…
Firstly we derive peculiar spherical Weyl solutions, using a general spherically symmetric metric due to a massive charged object with definite mass and radius. Afterwards, we present new analytical solutions for relevant cosmological…
It is shown that analytically soluble bound states of the Schr\"odinger equation for a large class of systems relevant to atomic and molecular physics can be obtained by means of the Laplace transform of the confluent hypergeometric…
In this paper, we use some Fourier analysis techniques to find an exact solution to the Cauchy problem for the $n$-dimensional biwave equation in the upper half-space $\mathbb{R}^n\times [0,+\infty)$.
It has been found a simple procedure for the general solution of the time-independent Schr\"odinger equation (SE) with the help of quantization of potential area in one dimension without making any approximation. Energy values are not…
The present paper is devoted to consideration and discussion of a number of contradictions that take place in fundamental electrodynamics researches. A concept of the scalar-vector potential is introduced that allows us to avoid a number of…
We consider the Cauchy problem for one-dimensional p-system with damping of space-dependent coefficient. This system models the compressible flow through porous media in the Lagrangean coordinate. Our concern is an asymptotic behavior of…
The study points out that the traditional solutions to wave equation of dissipative wave and motion equation of block for a multi-degree-of-freedom mass spring damper system are the possible solutions, which are not necessarily objective…
Lagrangian of electronic liquid in magneto-inhomogeneous micro-conductor has been constructed. A corresponding Euler-Lagrange equation has been solved. It was shown that the described system has eigenmodes of spin polarization and total…
The Landau-Lifshitz form of the Lorentz-Abraham-Dirac equation in the presence of a plane wave of arbitrary shape and polarization is solved exactly and in closed form. The explicit solution is presented in the particular, paradigmatic…
The Casimir energy for a compact dielectric sphere is considered in a novel way, using the quantum statistical method introduced by H\oye - Stell and others. Dilute media are assumed. It turns out that this method is a very powerful one: we…
In this study, we present analytical solutions of the Schr\"odinger equation with the Multiparameter potential containing the different types of physical potential via the asymptotic iteration method (AIM) by applying a Pekeris-type…
Treating a boundary value problem in analytical fluid dynamics, translation of 2D steady Navier-Stokes equations to ordinary differential form leads to a second order equation of Riccati type. In the case of a compressible fluid with…
We extend the results of a work by L. H\"ormander in 1990 concerning the resolution of the characteristic Cauchy problem for second order wave equations with regular first order potentials. The geometrical background of this work was a…
In this paper, we obtain a result on the existence and uniqueness of global spherically symmetric classical solutions to the compressible isentropic Navier-Stokes equations with vacuum in a bounded domain or exterior domain {\Omega} of Rn(n…