scholarly journals Implementation of VSVO code for solving boundary value problems of Dirichlet and Neumann type

2015 ◽  
Author(s):  
Phang Pei See ◽  
Zanariah Abdul Majid
Keyword(s):  
Boundary Value Problems ◽  
Boundary Value ◽  
Neumann Type

scholarly journals Polyanalytic boundary value problems for planar domains with harmonic Green function

2021 ◽  
Vol 11 (3) ◽  
Author(s):  
Heinrich Begehr ◽  
Bibinur Shupeyeva
Keyword(s):  
Green Function ◽  
Boundary Value Problems ◽  
Arbitrary Order ◽  
Boundary Value ◽  
Planar Domains ◽  
Schwarz Problem ◽  
Bianalytic Functions ◽  
Neumann Type ◽  
The Neumann Problem ◽  
Well Posed

AbstractThere are three basic boundary value problems for the inhomogeneous polyanalytic equation in planar domains, the well-posed iterated Schwarz problem, and further two over-determined iterated problems of Dirichlet and Neumann type. These problems are investigated in planar domains having a harmonic Green function. For the Schwarz problem, treated earlier [Ü. Aksoy, H. Begehr, A.O. Çelebi, AV Bitsadze’s observation on bianalytic functions and the Schwarz problem. Complex Var Elliptic Equ 64(8): 1257–1274 (2019)], just a modification is mentioned. While the Dirichlet problem is completely discussed for arbitrary order, the Neumann problem is just handled for order up to three. But a generalization to arbitrary order is likely.

scholarly journals TWO-DIMENSIONAL HYBRIDS WITH MIXED BOUNDARY VALUE PROBLEMS

2016 ◽  
Vol 56 (3) ◽  
pp. 245
Author(s):  
Marzena Szajewska ◽  
Agnieszka Tereszkiewicz
Keyword(s):  
Boundary Value Problems ◽  
Special Functions ◽  
Mixed Boundary ◽  
Boundary Value ◽  
Neumann Boundary ◽  
Dirichlet Condition ◽  
Two Dimensional ◽  
Neumann Type ◽  
Neumann Boundary Value Problems ◽  
Real Euclidean Space

Boundary value problems are considered on a simplex <em>F</em> in the real Euclidean space R<sup>2</sup>. The recent discovery of new families of special functions, orthogonal on <em>F</em>, makes it possible to consider not only the Dirichlet or Neumann boundary value problems on <em>F</em>, but also the mixed boundary value problem which is a mixture of Dirichlet and Neumann type, ie. on some parts of the boundary of <em>F</em> a Dirichlet condition is fulfilled and on the other Neumann’s works.

Iterative bounds for the stable solutions of convex non-linear boundary value problems

1977 ◽  
Vol 76 (2) ◽  
pp. 81-94 ◽  
Author(s):  
J. W. Mooney ◽  
G. F. Roach
Keyword(s):  
Boundary Value Problems ◽  
Differential Expression ◽  
Boundary Value ◽  
Linear Boundary ◽  
Non Linear ◽  
Unstable Solutions ◽  
Neumann Type ◽  
Thermal Combustion ◽  
Stable Solutions ◽  
Image Position

SynopsisWe consider a class of convex non-linear boundary value problems of the formwhere L is a linear, uniformly elliptic, self-adjoint differential expression, f is a given non-linear function, B is a boundary differential expression of either Dirichlet or Neumann type and D is a bounded open domain with boundary ∂D. Particular problems of this class arise in the process of thermal combustion [8].In this paper we show that stable solutions of this class can be bounded from below (above) by a monotonically increasing (decreasing) sequence of Newton (Picard) iterates. The possibility of using these schemes to construct unstable solutions is also considered.

Pointwise bounds for the solutions of certain boundary-value problems

1951 ◽  
Vol 208 (1093) ◽  
pp. 170-175 ◽  
Keyword(s):  
Boundary Value Problems ◽  
Function Space ◽  
Scalar Product ◽  
Boundary Value ◽  
The Other ◽  
Green Functions ◽  
Regular Functions ◽  
Cutting Out ◽  
Neumann Type ◽  
The One

The boundary-value problems considered are of the Dirichlet-Neumann type. The method now given for obtaining pointwise bounds of the solution and its derivatives is a compromise between the methods of Diaz and Greenberg on the one hand and Maple and Synge on the other; it appears to be simpler than either. The solution having been located on a hypercircle in function space, the pointwise bounds are obtained by taking the scalar product of the solution by certain vectors (Green’s vectors). Divergence of integrals due to the poles of the Green functions is avoided by the use of regular functions matching the Green functions on the boundary (Diaz-Greenberg device) instead of by cutting out spheres from the domain (Maple-Synge device).

SOLVABILITY OF NEUMANN TYPE NON-HOMOGENEOUS MULTI-POINT BVP FOR SECOND ORDER DIFFERENTIAL EQUATIONS WITH p-LAPLACIAN

2009 ◽  
Vol 07 (03) ◽  
pp. 279-295
Author(s):  
YUJI LIU
Keyword(s):  
Differential Equations ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
Sufficient Conditions ◽  
Second Order ◽  
Point Boundary ◽  
Second Order Differential Equations ◽  
Neumann Type

We consider the following multi-point boundary value problems [Formula: see text] New sufficient conditions to guarantee the existence of at least one solution of the above mentioned BVP are established. Two examples are presented to illustrate the main result.

Boundary value problems of stationary oscillation of thermoelasticity of microstretch materials with microtemperatures

2015 ◽  
Vol 22 (1) ◽  
Author(s):  
Levan Giorgashvili ◽  
Aslan Jaghmaidze ◽  
Giorgi Karseladze ◽  
Guram Sadunishvili
Keyword(s):  
Boundary Value Problems ◽  
Boundary Value ◽  
Representation Formula ◽  
Convergent Series ◽  
Homogeneous System ◽  
Stationary Oscillation ◽  
Neumann Type ◽  
Uniformly Convergent ◽  
Type Boundary ◽  
Linear Thermoelasticity

AbstractWe consider the stationary oscillation case of the theory of linear thermoelasticity with microtemperatures of microstretch materials. A representation formula of a general solution of a homogeneous system of differential equations is written in terms of eight metaharmonic functions. Such formulas are very convenient and useful in many specific problems of concrete geometry. We demonstrate an application of these formulas to Dirichlet and Neumann type boundary value problems in a ball. Explicit solutions in the form of absolutely and uniformly convergent series are constructed.

scholarly journals Non-trivial solutions of local and non-local Neumann boundary-value problems

2016 ◽  
Vol 146 (2) ◽  
pp. 337-369 ◽  
Author(s):  
Gennaro Infante ◽  
Paolamaria Pietramala ◽  
F. Adrián F. Tojo
Keyword(s):  
Boundary Value Problems ◽  
Fixed Point Index ◽  
Boundary Value ◽  
Neumann Boundary ◽  
Linear Operators ◽  
Local Boundary ◽  
Hammerstein Integral Equations ◽  
Neumann Type ◽  
Non Local ◽  
Neumann Boundary Value Problems

We prove new results on the existence, non-existence, localization and multiplicity of non-trivial solutions for perturbed Hammerstein integral equations. Our approach is topological and relies on the classical fixed-point index. Some of the criteria involve a comparison with the spectral radius of some related linear operators. We apply our results to some boundary-value problems with local and non-local boundary conditions of Neumann type. We illustrate in some examples the methodologies used.

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