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 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 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.

An elliptic boundary value problem for strongly non-linear equations in unbounded domains

1977 ◽  
Vol 77 (3-4) ◽  
pp. 217-230 ◽  
Author(s):  
Vesa Mustonen
Keyword(s):  
Boundary Value Problem ◽  
Elliptic Boundary ◽  
Boundary Value ◽  
Linear Equations ◽  
Unbounded Domains ◽  
Elliptic Boundary Value Problem ◽  
Elliptic Boundary Value ◽  
Non Linear ◽  
Linear Elliptic Boundary ◽  
Non Linear Equations

SynopsisThe existence of a variational solution is shown for the strongly non-linear elliptic boundary value problem in unbounded domains. The proof is a generalisation to Orlicz-Sobolev space setting of the idea introduced in [15] for the equations involving polynomial non-linearities only.

scholarly journals Asymptotic behavior for non-autonomous stochastic plate equation on unbounded domains

2019 ◽  
Vol 17 (1) ◽  
pp. 1281-1302 ◽  
Author(s):  
Xiaobin Yao ◽  
Xilan Liu
Keyword(s):  
Asymptotic Behavior ◽  
Additive Noise ◽  
Upper Semicontinuity ◽  
Unbounded Domains ◽  
Asymptotic Behavior Of Solutions ◽  
Plate Equation ◽  
Uniform Estimates ◽  
Estimates Of Solutions ◽  
Random Attractors

Abstract We study the asymptotic behavior of solutions to the non-autonomous stochastic plate equation driven by additive noise defined on unbounded domains. We first prove the uniform estimates of solutions, and then establish the existence and upper semicontinuity of random attractors.

Sign in / Sign up

Export Citation Format

Share Document