Integral Representations for the Solution of Dynamic Bending of a Plate with Displacement-Traction Boundary Data

2003 ◽  
Vol 10 (3) ◽  
pp. 467-480
Author(s):  
Igor Chudinovich ◽  
Christian Constanda
Keyword(s):  
Existence And Uniqueness ◽  
Boundary Data ◽  
Boundary Integral Equations ◽  
Mixed Boundary ◽  
Mixed Boundary Conditions ◽  
Boundary Integral ◽  
Integral Representations ◽  
Transverse Shear Deformation ◽  
Uniqueness Of Solutions ◽  
Nonstationary Boundary

Abstract The existence of distributional solutions is investigated for the time-dependent bending of a plate with transverse shear deformation under mixed boundary conditions. The problem is then reduced to nonstationary boundary integral equations and the existence and uniqueness of solutions to the latter are studied in appropriate Sobolev spaces.

Existence and Uniqueness of Solutions in Strain Space of Elastoplastic Problems with Isotropic Hardening

1997 ◽  
Vol 07 (01) ◽  
pp. 31-48 ◽  
Author(s):  
Ivan Hlaváček ◽  
John R. Whiteman
Keyword(s):  
Existence And Uniqueness ◽  
Mixed Boundary ◽  
Maximal Monotone ◽  
Maximal Monotone Operators ◽  
Mixed Boundary Conditions ◽  
Monotone Operators ◽  
Isotropic Hardening ◽  
Uniqueness Of Solutions ◽  
Quasistatic Problem ◽  
Strain Space

The flow theory of elasto-plastic bodies with isotropic strain hardening is formulated in strain space by means of a time-dependent variational inequality. Using concepts of subdifferential and multivalued maximal monotone operators, we prove the existence and uniqueness of a solution of the quasistatic problem in ℝn, (n = 2,3), with mixed boundary conditions.

scholarly journals Existence and uniqueness of solutions for a fractional boundary value problem on a graph

2014 ◽  
Vol 17 (2) ◽  
Author(s):  
John Graef ◽  
Lingju Kong ◽  
Min Wang
Keyword(s):  
Boundary Value Problem ◽  
Existence And Uniqueness ◽  
Fixed Point Theory ◽  
Mixed Boundary ◽  
Boundary Value ◽  
Mixed Boundary Conditions ◽  
Point Theory ◽  
Star Graph ◽  
Fractional Boundary Value Problem ◽  
Uniqueness Of Solutions

AbstractIn this paper, the authors consider a nonlinear fractional boundary value problem defined on a star graph. By using a transformation, an equivalent system of fractional boundary value problems with mixed boundary conditions is obtained. Then the existence and uniqueness of solutions are investigated by fixed point theory.

scholarly journals Solution of a Problem Linear Plane Elasticity with Mixed Boundary Conditions by the Method of Boundary Integrals

2014 ◽  
Vol 2014 ◽  
pp. 1-11
Author(s):  
Nahed S. Hussein
Keyword(s):  
Boundary Conditions ◽  
Boundary Integral Equations ◽  
Mixed Boundary ◽  
Stress Component ◽  
Mixed Boundary Conditions ◽  
Plane Elasticity ◽  
Boundary Integral ◽  
Unknown Boundary ◽  
Algebraic Equations ◽  
Boundary Values

A numerical boundary integral scheme is proposed for the solution to the system of…eld equations of plane. The stresses are prescribed on one-half of the circle, while the displacements are given. The considered problem with mixed boundary conditions in the circle is replaced by two problems with homogeneous boundary conditions, one of each type, having a common solution. The equations are reduced to a system of boundary integral equations, which is then discretized in the usual way, and the problem at this stage is reduced to the solution to a rectangular linear system of algebraic equations. The unknowns in this system of equations are the boundary values of four harmonic functions which define the full elastic solution and the unknown boundary values of stresses or displacements on proper parts of the boundary. On the basis of the obtained results, it is inferred that a stress component has a singularity at each of the two separation points, thought to be of logarithmic type. The results are discussed and boundary plots are given. We have also calculated the unknown functions in the bulk directly from the given boundary conditions using the boundary collocation method. The obtained results in the bulk are discussed and three-dimensional plots are given. A tentative form for the singular solution is proposed and the corresponding singular stresses and displacements are plotted in the bulk. The form of the singular tangential stress is seen to be compatible with the boundary values obtained earlier. The efficiency of the used numerical schemes is discussed.

scholarly journals Existence and uniqueness of positive solutions for nonlinear fractional mixed problems

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Alberto Cabada ◽  
Om Kalthoum Wanassi
Keyword(s):  
Existence And Uniqueness ◽  
Fixed Point Theory ◽  
Mixed Boundary ◽  
Point Theory ◽  
Uniqueness Of Solutions ◽  
Nonlinear Part ◽  
Banach Contraction ◽  
Fractional Differential ◽  
Exhaustive Study ◽  
The Banach Contraction Principle

Abstract This paper is devoted to study the existence and uniqueness of solutions of a one parameter family of nonlinear Riemann–Liouville fractional differential equations with mixed boundary value conditions. An exhaustive study of the sign of the related Green’s function is carried out. Under suitable assumptions on the asymptotic behavior of the nonlinear part of the equation at zero and at infinity, and by application of the fixed point theory of compact operators defined in suitable cones, it is proved that there exists at least one solution of the considered problem. Moreover, the method of lower and upper solutions is developed and the existence of solutions is deduced by a combination of both techniques. In particular cases, the Banach contraction principle is used to ensure the uniqueness of solutions.

scholarly journals Numerical solution of an elliptic 3-dimensional Cauchy problem by the alternating method and boundary integral equations

2016 ◽  
Vol 24 (6) ◽  
Author(s):  
Ihor Borachok ◽  
Roman Chapko ◽  
B. Tomas Johansson
Keyword(s):  
Cauchy Problem ◽  
Integral Equations ◽  
Boundary Integral Equations ◽  
Mixed Boundary ◽  
Single Layer ◽  
Normal Derivative ◽  
Boundary Integral ◽  
Iteration Step ◽  
3 Dimensional ◽  
Boundary Surfaces

AbstractWe consider the Cauchy problem for the Laplace equation in 3-dimensional doubly-connected domains, that is the reconstruction of a harmonic function from knowledge of the function values and normal derivative on the outer of two closed boundary surfaces. We employ the alternating iterative method, which is a regularizing procedure for the stable determination of the solution. In each iteration step, mixed boundary value problems are solved. The solution to each mixed problem is represented as a sum of two single-layer potentials giving two unknown densities (one for each of the two boundary surfaces) to determine; matching the given boundary data gives a system of boundary integral equations to be solved for the densities. For the discretisation, Weinert’s method [

BOUNDARY INTEGRAL EQUATIONS FOR A THREE-DIMENSIONAL STOKES–BRINKMAN CELL MODEL

2008 ◽  
Vol 18 (12) ◽  
pp. 2055-2085 ◽  
Author(s):  
MIRELA KOHR ◽  
G. P. RAJA SEKHAR ◽  
WOLFGANG L. WENDLAND
Keyword(s):  
Stokes Flow ◽  
Existence And Uniqueness ◽  
Stokes Equations ◽  
Boundary Integral Equations ◽  
Cell Model ◽  
Uniqueness Result ◽  
Boundary Integral ◽  
Porous Particle ◽  
Brinkman Equation ◽  
Special Cases

The purpose of this paper is to prove the existence and uniqueness of the solution in Sobolev or Hölder spaces for a cell model problem which describes the Stokes flow of a viscous incompressible fluid in a bounded region past a porous particle. The flow within the porous particle is described by the Brinkman equation. In order to obtain the desired existence and uniqueness result, we use an indirect boundary integral formulation and potential theory for both Brinkman and Stokes equations. Some special cases, which refer to the cell model for a porous particle with large permeability, or to the exterior Stokes flow past a porous particle, are also presented.

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