scholarly journals On solvability of boundary value problem for elliptic equations with Bitsadze-Samarskiĭ condition

1988 ◽  
Vol 11 (1) ◽  
pp. 101-113 ◽  
Author(s):  
J. H. Chabrowski
Keyword(s):  
Boundary Value Problem ◽  
Weak Solutions ◽  
Elliptic Equations ◽  
Existence And Uniqueness ◽  
Weighted Sobolev Space ◽  
Boundary Value ◽  
Linear Elliptic Equation ◽  
Crucial Point ◽  
Non Local ◽  
Suitable Modification

In this paper we investigate the solvability of a non-local problem for a linear elliptic equation, which is also known as the boundary value problem with the Bitsadze-Samarskiĭ condition. We prove the existence and uniqueness of a classical solution to this problem. In the final part of this paper we propose anL2-approach which gives a rise to weak solutions in a weighted Sobolev space. The crucial point in proving the existence of weak solutions is a suitable modification of the Bitsadze-Samarskiĭ condition.

EXISTENCE AND UNIQUENESS OF WEAK AND CLASSICAL SOLUTIONS FOR A FOURTH-ORDER SEMILINEAR BOUNDARY VALUE PROBLEM

2019 ◽  
Vol 61 (3) ◽  
pp. 305-319
Author(s):  
CRISTIAN-PAUL DANET
Keyword(s):  
Boundary Value Problem ◽  
Variational Methods ◽  
Fourth Order ◽  
Weak Solutions ◽  
Existence And Uniqueness ◽  
Boundary Value ◽  
Classical Solutions ◽  
Maximum Principles ◽  
Uniqueness Results

This paper is concerned with the problem of existence and uniqueness of weak and classical solutions for a fourth-order semilinear boundary value problem. The existence and uniqueness for weak solutions follows from standard variational methods, while similar uniqueness results for classical solutions are derived using maximum principles.

Existence and uniqueness of weak and classical solutions for a fourth-order semilinear boundary value problem

2019 ◽  
Vol 61 ◽  
pp. 305-319
Author(s):  
Cristian Paul Danet
Keyword(s):  
Boundary Value Problem ◽  
Variational Methods ◽  
Fourth Order ◽  
Weak Solutions ◽  
Existence And Uniqueness ◽  
Boundary Value ◽  
Classical Solutions ◽  
Maximum Principles ◽  
Uniqueness Results

This paper is concerned with the problem of existence and uniqueness of weak and classical solutions for a fourth-order semilinear boundary value problem. The existence and uniqueness for weak solutions follows from standard variational methods, while similar uniqueness results for classical solutions are derived using maximum principles. doi:10.1017/S1446181119000129

NON-NEWTONIAN STOKES FLOW WITH FRICTIONAL BOUNDARY CONDITIONS

2007 ◽  
Vol 12 (4) ◽  
pp. 483-495 ◽  
Author(s):  
Fouad Saidi
Keyword(s):  
Fluid Flow ◽  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Variational Inequalities ◽  
Newtonian Fluid ◽  
Stokes Flow ◽  
Weak Solutions ◽  
Existence And Uniqueness ◽  
Boundary Value

In this work we deal with the boundary value problem for the non‐Newtonian fluid flow with boundary conditions of friction type, mostly by means of variational inequalities. Among others, theorems concerning existence and uniqueness or non‐uniqueness of weak solutions are presented.

scholarly journals Weak solutions in Elasticity of dipolar bodies with stretch

2013 ◽  
Vol 29 (1) ◽  
pp. 33-40
Author(s):  
MARIN MARIN ◽  
◽  
GABRIEL STAN ◽  
Keyword(s):  
Weak Solution ◽  
Boundary Value Problem ◽  
Weak Solutions ◽  
Existence And Uniqueness ◽  
Boundary Value ◽  
Linear Operators ◽  
Elastic Materials ◽  
Elastic Bodies ◽  
Dipolar Bodies

In the present paper we generalize the results obtained by Iesan and Quintanilla for microstretch elastic bodies in order to cover the dipolar elastic materials with stretch. For the boundary value problem considered in this context, we use some results from the theory of semigroups of the linear operators in order to prove the existence and uniqueness of a weak solution.

scholarly journals Weak Solutions in Elasticity of Dipolar Porous Materials

2008 ◽  
Vol 2008 ◽  
pp. 1-8 ◽  
Author(s):  
Marin Marin
Keyword(s):  
General Theory ◽  
Porous Materials ◽  
Boundary Value Problems ◽  
Weak Solutions ◽  
Elliptic Equations ◽  
Existence And Uniqueness ◽  
Boundary Value ◽  
Generalized Solutions

The main aim of our study is to use some general results from the general theory of elliptic equations in order to obtain some qualitative results in a concrete and very applicative situation. In fact, we will prove the existence and uniqueness of the generalized solutions for the boundary value problems in elasticity of initially stressed bodies with voids (porous materials).

scholarly journals The Existence and Uniqueness of a New Boundary Value Problem (Type of Problem “E”) for Linear System Equations of the Mixed Hyperbolic-Elliptic Type in the Multivariate Dimension with the Changing Time Direction

2015 ◽  
Vol 2015 ◽  
pp. 1-10
Author(s):  
Mahammad A. Nurmammadov
Keyword(s):  
Functional Analysis ◽  
Boundary Value Problem ◽  
Existence And Uniqueness ◽  
Weighted Sobolev Space ◽  
Boundary Value ◽  
Elliptic Type ◽  
Problem Type ◽  
Regular Solutions ◽  
Time Direction ◽  
System Equations

The existence and uniqueness of the boundary value problem for linear systems equations of the mixed hyperbolic-elliptic type in the multivariate domain with the changing time direction are studied. Applying methods of functional analysis, “ε-regularizing” continuation by the parameter and by means of prior estimates, the existence and uniqueness of generalized and regular solutions of a boundary problem are established in a weighted Sobolev space.

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