相关论文: Generalized axially symmetric potentials with dist…

In this paper, we present a unified analysis of the superconvergence property for a large class of mixed discontinuous Galerkin methods. This analysis applies to both the Poisson equation and linear elasticity problems with symmetric stress…

In this note we discuss an abstract framework for standard boundary value problems in divergence form with maximal monotone relations as "coefficients". A reformulation of the respective problems is constructed such that they turn out to be…

In the framework of Clifford analysis, a chain of harmonic and monogenic potentials is constructed in the upper half of Euclidean space $\mR^{m+1}$, including a higher dimensional generalization of the complex logarithmic function. Their…

This monograph presents a comprehensive treatment of second order divergence form elliptic operators with bounded measurable t-independent coefficients in spaces of fractional smoothness, in Besov and weighted Sobolev classes. We establish…

Solutions for a class of wave equations with effective potentials are obtained by a method of a Laplace-transform. Quasinormal modes appear naturally in the solutions only in a spatially truncated form; their coefficients are uniquely…

The inversion theorem and convolution theorem of the conformable fractional Laplace transforms are developed. All the elementary properties of the classical Laplace transform are extended to the conformable fractional transform, and using…

In this paper, we study boundary-value problems describing the exit distribution of finite-velocity random motions from prescribed domains. For the standard telegraph process, with and without drift, we derive the Dirichlet problems…

We present a construction of a multi-scale Gaussian beam parametrix for the Dirichlet boundary value problem associated with the wave equation, and study its convergence rate to the true solution in the highly oscillatory regime. The…

The diffuse-domain, or smoothed boundary, method is an attractive approach for solving partial differential equations in complex geometries because of its simplicity and flexibility. In this method the complex geometry is embedded into a…

In this article, we derive the asymptotic expansion, up to an arbitrary order in theory, for the solution of a two-dimensional elliptic equation with strongly anisotropic diffusion coefficients along different directions, subject to the…

Dirac equation is solved for some exponential potentials, hypergeometric-type potential, generalized Morse potential and Poschl-Teller potential with any spin-orbit quantum number $\kappa$ in the case of spin and pseudospin symmetry,…

We study existence, uniqueness, and distributional aspects of generalized solutions to the Cauchy problem for first-order symmetric (or Hermitian) hyperbolic systems of partial differential equations with Colombeau generalized functions as…

We continue the development, by reduction to a first order system for the conormal gradient, of $L^2$ \textit{a priori} estimates and solvability for boundary value problems of Dirichlet, regularity, Neumann type for divergence form second…

In this paper, we study a class of fractional Schr\"{o}dinger equation \begin{equation} \label{eq0} \left\{ \begin{aligned} &(-\Delta)^{s}u=\lambda u+a(x)|u|^{p-2}u,\\ &\int_{\mathbb{R}^{N}}|u|^{2}dx=c^{2},\ u\in H^{s}(\mathbb{R}^{N}),…

We construct a class of global, dynamical solutions to the 3d Euler equations near the stationary state given by uniform "rigid body" rotation. These solutions are axisymmetric, of Sobolev regularity, have non-vanishing swirl and scatter…

We prove weighted analytic regularity of solutions to the Dirichlet problem for the integral fractional Laplacian in polygons with analytic right-hand side. We localize the problem through the Caffarelli-Silvestre extension and study the…

In his deep and prolific investigations of heat diffusion, Lam\'e was led to the investigation of the eigenvalues and eigenfunctions of the Laplace operator in an equilateral triangle. In particular he derived explicit results for the…

The generalized Laplace (GL) distribution, which falls in the larger family of generalized hyperbolic distributions, provides a versatile model to deal with a variety of applications thanks to its shape parameters. The elliptically…

This paper is concerned with the limit laws of the extreme order statistics derived from a symmetric Laplace walk. We provide two different descriptions of the point process of the limiting extreme order statistics: a branching…

The exact analytical solutions of the Schr\"odinger equation for the generalized symmetrical Woods-Saxon potential are examined for the scattering, bound and quasi-bound states in one dimension. The reflection and transmission coefficients…