On sufficient solvability conditions for Neumann type problems for polyharmonic equation in a ball

2021 ◽  
Author(s):  
Batirkhan Turmetov ◽  
Valery Karachik
Keyword(s):  
Polyharmonic Equation ◽  
Solvability Conditions ◽  
Neumann Type

Boundary value problems for the inhomogeneous polyanalytic equation I

Analysis ◽  
2005 ◽  
Vol 25 (1) ◽  
Author(s):  
Heinrich Begehr ◽  
Ajay Kumar
Keyword(s):  
Boundary Conditions ◽  
Boundary Value Problems ◽  
Complex Analysis ◽  
Boundary Value ◽  
Higher Order ◽  
Solvability Conditions ◽  
Neumann Type ◽  
Well Posed ◽  
Basic Boundary

AbstractThe three basic boundary value problems in complex analysis are of Schwarz, of Dirichlet and of Neumann type. When higher order equations are investigated all kind of combinations of these boundary conditions are proper to determine solutions. However, not all of these conditions are leading to well-posed problems. Some are overdetermined so that solvability conditions have to be found. Some of these boundary value problems are treated here for the inhomogeneous polyanalytic equation.

Stability of Implicit Difference Equations Generated by Parabolic Functional Differential Problems

2007 ◽  
Vol 7 (1) ◽  
pp. 68-82
Author(s):  
K. Kropielnicka
Keyword(s):  
Differential Equations ◽  
Functional Differential Equations ◽  
Initial Boundary ◽  
Numerical Examples ◽  
Convergence Results ◽  
Nonlinear Parabolic ◽  
Implicit Difference Methods ◽  
Neumann Type ◽  
Difference Methods ◽  
Functional Differential

AbstractA general class of implicit difference methods for nonlinear parabolic functional differential equations with initial boundary conditions of the Neumann type is constructed. Convergence results are proved by means of consistency and stability arguments. It is assumed that given functions satisfy nonlinear estimates of Perron type with respect to functional variables. Differential equations with deviated variables and differential integral problems can be obtained from a general model by specializing given operators. The results are illustrated by numerical examples.

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