Results 61 to 70 of about 2,300,828 (212)

Eigenfunctions and Fundamental Solutions of the Fractional Two-Parameter Laplacian

International Journal of Mathematics and Mathematical Sciences, 2010
We deal with the following fractional generalization of the Laplace equation for rectangular domains (x,y)∈(x0,X0)×(y0,Y0)⊂ℝ+×ℝ+, which is associated with the Riemann-Liouville fractional derivatives Δα,βu(x,y)=λu(x,y), Δα,β:=Dx0+1+α+Dy0+1+β, where λ∈ℂ, (
Semyon Yakubovich
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On the Fundamental Solution of the Reduced Wave Equation

Journal of King Saud University: Engineering Sciences, 1995
A method is presented for constructing fundamental solutions for the Helmholtz operators Δ ± k2 in Rn in terms of the fundamental singularity for the Laplacian Δ.
M.A. Al-Gwaiz
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Fundamental matrix of solutions for one class of parabolic degenerate systems

Karpatsʹkì Matematičnì Publìkacìï, 2013
We consider one class of ultraparabolic equation systems of second order, that have three groups of degenerated variables and coefficients of which depend only on a time variable.
I. V. Burtnyak, H. P. Malytska
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On a boundary value problem to third order PDE with multiple characteristics

Nonlinear Analysis, 2011
In the paper the second boundary value problem in a rectangular domain to equation uxxx − uyy = f(x, y) with the multiple characteristics is considered. The considered equation is closely related with nonlinear equation uxxx + uyy −(ν/y)uy = uxuxx, which
Yusufjon P. Apakov, Stasys Rutkauskas
doaj  

On the fundamental solutions of a discontinuous fractional boundary value problem

Advances in Difference Equations, 2017
The main purpose of this study is to investigate a fractional discontinuous Sturm-Liouville problem with transmission conditions. We shall consider a fractional boundary value problem involving an operator with two parts. It is shown that the eigenvalues
Ali Yakar, Zulfigar Akdogan
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On the Behaviour at Infinity of Solutions to Nonlocal Parabolic Type Problems

Известия Иркутского государственного университета: Серия "Математика", 2019
The paper deals with possible behaviour at infinity of solutions to the Cauchy problem for a parabolic type equation whose elliptic part is the generator of a Markov jump process , i.e. a nonlocal diffusion operator.
Е. А. Zhizhina, А. L. Piatnitski
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Representation Formula for Solutions of Eikonal Type Equations

Nonlinear Analysis, 2001
Equations of an eikonal type ones arise in many areas of applications, including optics, fluid mechanics, material sciences, and control theory. This article investigates the representation formula for semiconcave solutions of the boundary problem for ...
Gintautas Gudynas
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The Stress-Strain State of the Tribo-Fatigue System Roller-Shaft

Механика машин, механизмов и материалов, 2013
Tribo-fatigue system roller-shaft, working in conditions of contact interaction between the roller and the shaft and the non-contact bending shaft is considered.
S.S. Shcherbakov
doaj  

Method of fundamental solutions for a conductivity problem

Applied Mathematics in Science and Engineering
A numerical solution of the interior Dirichlet problem for the homogeneous conductivity equation is considered. After introducing certain assumptions and discretization of the domain, the boundary value problem for a second-order elliptic equation with ...
Andriy Beshley, Ihor Borachok
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Branching of automorphic fundamental solutions

Michigan Mathematical Journal, 2015
10 pages, 1 figure. Augmented introduction, other minor changes to improve clarity.
openaire   +3 more sources