scholarly journals About Three Dimensional Jump Boundary Value Problems for the Laplacian

2019 ◽  
pp. 51-54
Author(s):  
Olexandr Polishchuk
Keyword(s):  
Hilbert Space ◽  
Integral Equation ◽  
Boundary Value Problems ◽  
Three Dimensional ◽  
Boundary Surface ◽  
Equation System ◽  
Normal Derivative ◽  
Layer Potentials ◽  
Jump Problem ◽  
Well Posed

The conditions of well-posed solvability of searched function and its normal derivative three dimensional jump problem for the Laplacian and equivalent to them integral equation system for the sum of the simple and double layer potentials are determined in the Hilbert space, element of which as well as their normal derivatives have the jump through boundary surface.

scholarly journals A unified boundary integral equation method for a class of second order elliptic boundary value problems

1984 ◽  
Vol 25 (4) ◽  
pp. 501-517 ◽  
Author(s):  
M. Rezayat ◽  
F. J. Rizzo ◽  
D. J. Shippy
Keyword(s):  
Integral Equation ◽  
Boundary Value Problems ◽  
Elliptic Boundary ◽  
Boundary Value ◽  
Three Dimensional ◽  
Integral Equation Method ◽  
Boundary Integral ◽  
Second Order ◽  
Elliptic Type ◽  
Integral Equation Formulation

AbstractA generalized integral equation formulation and a systematic numerical solution procedure are presented for a class of boundary value problems governed by a general second-order differential equation of elliptic type. Diverse numerical examples include problems of plane-wave scattering, three-dimensional fluid flow, and plane heat transfer for a body with a moving flame boundary. The last example employs certain representation functions useful to increase solution effectiveness in problems with an isolated integrable singularity.

scholarly journals Boundary value problems for second-order partial differential equations with operator coefficients

2001 ◽  
Vol 6 (5) ◽  
pp. 253-266
Author(s):  
Kudratillo S. Fayazov ◽  
Eberhard Schock
Keyword(s):  
Hilbert Space ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Boundary Value Problems ◽  
Linear Operators ◽  
Dense Domain ◽  
Simply Connected Region ◽  
Simply Connected ◽  
Well Posed ◽  
Stability Of The Solution

LetΩ Tbe some bounded simply connected region inℝ 2with∂ Ω T=Γ¯1∩Γ¯2. We seek a functionu(x,t)((x,t)∈Ω T)with values in a Hilbert spaceHwhich satisfies the equationALu(x,t)=Bu(x,t)+f(x,t,u,u t),(x,t)∈Ω T, whereA(x,t),B(x,t)are families of linear operators (possibly unbounded) with everywhere dense domainD(Ddoes not depend on(x,t)) inHandLu(x,t)=u tt+a 11u xx+a 1u t+a 2u x. The valuesu(x,t);∂u(x,t)/∂nare given inΓ 1. This problem is not in general well posed in the sense of Hadamard. We give theorems of uniqueness and stability of the solution of the above problem.

Three-Dimensional Boundary Value Problems of Elastothermodiffusion with Mixed Boundary Conditions

1997 ◽  
Vol 4 (3) ◽  
pp. 243-258
Author(s):  
T. Burchuladze ◽  
Yu. Bezhuashvili
Keyword(s):  
Boundary Conditions ◽  
Boundary Value Problems ◽  
Singular Integrals ◽  
Mixed Boundary ◽  
Boundary Value ◽  
Three Dimensional ◽  
Boundary Surface ◽  
Mixed Boundary Conditions ◽  
Theory Of Elasticity ◽  
Classical Solutions

Abstract We investigate the basic boundary value problems of the connected theory of elastothermodiffusion for three-dimensional domains bounded by several closed surfaces when the same boundary conditions are fulfilled on every separate boundary surface, but these conditions differ on different groups of surfaces. Using the results of papers [Kupradze, Gegelia, Basheleishvili, and Burchuladze, Three-dimensional problems of the mathematical theory of elasticity and thermoelasticity, North-Holland Publishing Company, 1979, Russian original, 1976–Mikhlin, Multi-dimensional singular integrals and integral equations, 1962], we prove theorems on the existence and uniqueness of the classical solutions of these problems.

scholarly journals On the Modified Jump Problem for the Laplace Equation in the Exterior of Cracks in a Plane

2012 ◽  
Vol 2012 ◽  
pp. 1-12 ◽  
Author(s):  
P. A. Krutitskii ◽  
A. Sasamoto
Keyword(s):  
Boundary Condition ◽  
Integral Equation ◽  
Boundary Value Problem ◽  
Integral Representation ◽  
Classical Solution ◽  
Laplace Equation ◽  
Normal Derivative ◽  
Index Zero ◽  
Jump Problem ◽  
Unique Classical Solution

The boundary value problem for the Laplace equation outside several cracks in a plane is studied. The jump of the solution of the Laplace equation and the boundary condition containing the jump of its normal derivative are specified on the cracks. The problem has unique classical solution under certain conditions. The new integral representation for the unique solution of this problem is obtained. The problem is reduced to the uniquely solvable Fredholm equation of the second kind and index zero. The integral representation and integral equation are essentially simpler than those derived for this problem earlier. The singularities at the ends of the cracks are investigated.

Sign in / Sign up

Export Citation Format

Share Document