scholarly journals Mixed Boundary Value Problems for the Elasticity System in Exterior Domains

2019 ◽  
Vol 24 (2) ◽  
pp. 58
Author(s):  
Hovik A. Matevossian
Keyword(s):  
Asymptotic Behavior ◽  
Variational Principle ◽  
Mixed Boundary ◽  
Asymptotic Behavior Of Solutions ◽  
Compact Set ◽  
Uniqueness Theorems ◽  
Energy Integral ◽  
Exterior Domains ◽  
Mixed Problems ◽  
Elasticity System

We study the properties of solutions of the mixed Dirichlet–Robin and Neumann–Robin problems for the linear system of elasticity theory in the exterior of a compact set and the asymptotic behavior of solutions of these problems at infinity under the assumption that the energy integral with weight | x | a is finite for such solutions. We use the variational principle and depending on the value of the parameter a, obtain uniqueness (non-uniqueness) theorems of the mixed problems or present exact formulas for the dimension of the space of solutions.

scholarly journals On the Mixed Dirichlet–Steklov-Type and Steklov-Type Biharmonic Problems in Weighted Spaces

2019 ◽  
Vol 24 (1) ◽  
pp. 25 ◽  
Author(s):  
Hovik Matevossian
Keyword(s):  
Asymptotic Behavior ◽  
Elliptic Boundary ◽  
Unbounded Domains ◽  
Generalized Solutions ◽  
Asymptotic Behavior Of Solutions ◽  
Compact Set ◽  
Uniqueness Theorems ◽  
Dirichlet Integral ◽  
Elliptic Boundary Value ◽  
Biharmonic Problems

We studied the properties of generalized solutions in unbounded domains and the asymptotic behavior of solutions of elliptic boundary value problems at infinity. Moreover, we studied the unique solvability of the mixed Dirichlet–Steklov-type and Steklov-type biharmonic problems in the exterior of a compact set under the assumption that generalized solutions of these problems has a bounded Dirichlet integral with weight | x | a . Depending on the value of the parameter a, we obtained uniqueness (non-uniqueness) theorems of these problems or present exact formulas for the dimension of the space of solutions.

scholarly journals On Some Properties of Solutions of Polyharmonic Equation in Polyhedral Angles

2007 ◽  
Vol 14 (3) ◽  
pp. 565-580
Author(s):  
Ilia Tavkhelidze
Keyword(s):  
Differential Equation ◽  
Asymptotic Behavior ◽  
Boundary Value Problems ◽  
Order Differential Equation ◽  
Fundamental Solutions ◽  
Asymptotic Behavior Of Solutions ◽  
Uniqueness Theorems ◽  
Energy Integral ◽  
Polyharmonic Operator ◽  
Polyharmonic Equation

Abstract For a higher order differential equation with the polyharmonic operator, the Dirichlet and Riquier boundary value problems are studied in some polyhedral angles. Uniqueness theorems for solutions with a bounded “energy integral” of the corresponding BVPs are proved. Recurrent formulas are constructed for representation of fundamental solutions and Green's functions. The asymptotic behavior of solutions at infinity is studied.

scholarly journals On the Asymptotic Behavior of D-Solutions to the Displacement Problem of Linear Elastostatics in Exterior Domains

Mathematics ◽  
2020 ◽  
Vol 8 (1) ◽  
pp. 77
Author(s):  
Vincenzo Coscia
Keyword(s):  
Asymptotic Behavior ◽  
Lipschitz Domain ◽  
Three Dimensional ◽  
Finite Energy ◽  
Asymptotic Behavior Of Solutions ◽  
Exterior Domains ◽  
Displacement Problem ◽  
Linear Elastostatics

We study the asymptotic behavior of solutions with finite energy to the displacement problem of linear elastostatics in a three-dimensional exterior Lipschitz domain.

scholarly journals On the Mixed Dirichlet--Farwig biharmonic problem in exterior domains

2019 ◽  
Vol 16 ◽  
pp. 8322-8329
Author(s):  
Hovik A. Matevossian
Keyword(s):  
Elliptic Boundary ◽  
Unbounded Domains ◽  
Generalized Solutions ◽  
Asymptotic Behavior Of Solutions ◽  
Variation Principle ◽  
Compact Set ◽  
Exterior Domains ◽  
Dirichlet Integral ◽  
Elliptic Boundary Value ◽  
Biharmonic Problem

We study the properties of generalized solutions in unbounded domains and the asymptotic behavior of solutions of elliptic boundary value problems at infinity. Moreover, we study the unique solvability of the mixed Dirichlet--Farwig biharmonic problem in the exterior of a compact set under the assumption that generalized solutions of these problems has a bounded Dirichlet integral with weight $|x|^a$. Admitting different boundary conditions, we used the variation principle and depending on the value of the parameter $a$, we obtained uniqueness (non-uniqueness) theorems of the problem or present exact formulas for the dimension of the space of solutions.

scholarly journals Asymptotics and Uniqueness of Solutions of the Elasticity System with the Mixed Dirichlet–Robin Boundary Conditions

Mathematics ◽  
2020 ◽  
Vol 8 (12) ◽  
pp. 2241
Author(s):  
Hovik A. Matevossian
Keyword(s):  
Generalized Solutions ◽  
Asymptotic Behavior Of Solutions ◽  
Robin Boundary Conditions ◽  
Uniqueness Theorems ◽  
Robin Problem ◽  
Uniqueness Of Solutions ◽  
Main Method ◽  
Elasticity System ◽  
Robin Boundary ◽  
Admissible Functions

We study properties of generalized solutions of the Dirichlet–Robin problem for an elasticity system in the exterior of a compact, as well as the asymptotic behavior of solutions of this mixed problem at infinity, with the condition that the energy integral with the weight |x|a is finite. Depending on the value of the parameter a, we have proved uniqueness (or non-uniqueness) theorems for the mixed Dirichlet–Robin problem, and also given exact formulas for the dimension of the space of solutions. The main method for studying the problem under consideration is the variational principle, which assumes the minimization of the corresponding functional in the class of admissible functions.

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