相关论文: An explicit factorization of the Green's function …

We show that the acoustic Green`s function for a half-space impedance problem in arbitrary spatial dimension d can be written as a sum of two terms, each of which is the product of an exponential function with the eikonal in the argument…

This article is devoted to deduce the expression of the Green's function related to a general constant coefficients fractional difference equation coupled to Dirichlet conditions. In this case, due to the points where some of the fractional…

A classical problem in acoustic (and electromagnetic) scattering concerns the evaluation of the Green's function for the Helmholtz equation subject to impedance boundary conditions on a half-space. The two principal approaches used for…

Acoustic room modes and the Green's function mode expansion are well-known for rectangular rooms with perfectly reflecting walls. First-order approximations also exist for nearly rigid boundaries; however, current analytical methods fail to…

During the past three decades, the advantageous concept of the Green's function has been extended from linear systems to nonlinear ones. At that, there exist a rigorous and an approximate extensions. The rigorous extension introduces the…

Using Gegenbauer polynomials and the zonal harmonic functions we build an explicit representation formula for the Green function with Neumann boundary conditions in the annulus.

We use the newly introduced conformable fractional derivative, which is different from the Caputo and Riemann-Liouville fractional derivatives, to reformulate several common boundary value problems, including those with conjugate,…

In this paper we will show several properties of the Green's functions related to various boundary value problems of arbitrary even order. In particular, we will write the expression of the Green's functions related to the general…

We provide explicit representations of Green's functions for general linear fractional differential operators with {\it variable coefficients} and Riemann-Liouvilles derivatives. We assume that all their coefficients are continuous in $[0,…

We construct an expression for the Green function of a differential operator satisfying nonlocal, homogeneous boundary conditions starting from the fundamental solution of the differential operator. This also provides the solution to the…

In this paper we study some classes of second order non-homogeneous nonlinear differential equations allowing a specific representation for nonlinear Green's function. In particular, we show that if the nonlinear term possesses a special…

This paper presents an extended version of the article [Franz, S., Kopteva, N.: J. Differential Equations, 252 (2012)]. The main improvement compared to the latter is in that here we additionally estimate the mixed second-order derivative…

In this paper we are interested in obtaining the exact expression and the study of the constant sign of the Green's function related to a second order perturbed periodic problem coupled with integral boundary conditions at the extremes of…

A dynamic 3D Green's function for the homogeneous, isotropic and viscoelastic (of the Zener type) half-space is derived in a closed form. The results obtained here can be used as either stand-alone solutions for simple problems or in…

The electromagnetic Green's function is a crucial ingredient for the theoretical study of modern photonic quantum devices, but is often difficult or even impossible to calculate directly. We present a numerically efficient framework for…

Green's functions with continuum spectra are a way of avoiding the strong bounds on new physics from the absence of new narrow resonances in experimental data. We model such a situation with a five-dimensional model with two branes along…

We study semi-martingale obliquely reflected Brownian motion with drift in the first quadrant of the plane in the transient case. Our main result determines a general explicit integral expression for the moment generating function of…

Green's function plays a significant role in both theoretical analysis and numerical computing of partial differential equations (PDEs). However, in most cases, Green's function is difficult to compute. The troubles arise in the following…

This paper is concerned with the study of Green's functions for one dimensional diffusions with constant diffusion coefficient and linear time inhomogeneous drift. It is well know that the whole line Green's function is given by a Gaussian.…

A new perspective of the Green's function in a boundary value problem as the only eigenstate in an auxiliary formulation is introduced. In this treatment, the Green's function can be perceived as a defect state in the presence of a…