scholarly journals Continuous dependence results for non-linear Neumann type boundary value problems

2008 ◽  
Vol 245 (9) ◽  
pp. 2368-2396 ◽  
Author(s):  
Espen R. Jakobsen ◽  
Christine A. Georgelin
Keyword(s):  
Boundary Value Problems ◽  
Continuous Dependence ◽  
Boundary Value ◽  
Non Linear ◽  
Neumann Type ◽  
Type Boundary ◽  
Continuous Dependence Results

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.

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 Explicit Solutions of the Basic Boundary Value Problems of Statics of the Elastic Mixture Theory for an Annulus

2004 ◽  
Vol 11 (1) ◽  
pp. 49-58
Author(s):  
M. Basheleishvili
Keyword(s):  
Boundary Value Problems ◽  
Boundary Value ◽  
Mixture Theory ◽  
Convergent Series ◽  
Explicit Solutions ◽  
Neumann Type ◽  
Uniformly Convergent ◽  
Type Boundary ◽  
Solutions Of Equations ◽  
Basic Boundary

Abstract Using the complex representation formulae of regular solutions of equations of statics of the theory of elastic mixtures, we construct the explicit solutions of the Dirichlet and Neumann type boundary value problems for an annulus in the form of absolutely and uniformly convergent series.

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.

Direct integration of the third-order two point and multipoint Robin type boundary value problems

2021 ◽  
Vol 182 ◽  
pp. 411-427
Author(s):  
Nadirah Mohd Nasir ◽  
Zanariah Abdul Majid ◽  
Fudziah Ismail ◽  
Norfifah Bachok
Keyword(s):  
Boundary Value Problems ◽  
Boundary Value ◽  
Direct Integration ◽  
Third Order ◽  
The Third ◽  
Type Boundary
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