scholarly journals Problem of Statics of the Linear Thermoelasticity of the Microstretch Materials with Microtemperatures for a Half-space

2021 ◽  
pp. 202-219
Author(s):  
Maia Kharashvili ◽  
◽  
Ketevan Skhvitaridze
Keyword(s):  
Differential Equations ◽  
Boundary Value Problem ◽  
Half Space ◽  
Boundary Value ◽  
Representation Formula ◽  
Subject Classification ◽  
Uniqueness Theorems ◽  
Type Boundary ◽  
Linear Thermoelasticity

We consider the statics case of the theory of linear thermoelasticity with microtemperatures and microstrech materials. The representation formula of differential equations obtained in the paper is expressed by the means of four harmonic and four metaharmonic functions. These formulas are very convenient and useful in many particular problems for domains with concrete geometry. Here we demonstrate an application of these formulas to the III type boundary value problem for a half-space. Uniqueness theorems are proved. Solutions are obtained in quadratures. 2010 Mathematics Subject Classification. 74A15, 74B10, 74F20.

Method of Forced Monotonicity for Conjugate type Boundary Value Problems for Ordinary Differential Equations

1988 ◽  
Vol 31 (1) ◽  
pp. 79-84
Author(s):  
P. W. Eloe ◽  
P. L. Saintignon
Keyword(s):  
Differential Operator ◽  
Differential Equations ◽  
Boundary Value Problem ◽  
Ordinary Differential Equations ◽  
Linear Differential Operator ◽  
Boundary Value ◽  
Linear Differential ◽  
Type Boundary ◽  
Sign Conditions ◽  
Conjugate Type

AbstractLet I = [a, b] ⊆ R and let L be an nth order linear differential operator defined on Cn(I). Let 2 ≦ k ≦ n and let a ≦ x1 < x2 < … < xn = b. A method of forced mono tonicity is used to construct monotone sequences that converge to solutions of the conjugate type boundary value problem (BVP) Ly = f(x, y),y(i-1) = rij where 1 ≦i ≦ mj, 1 ≦ j ≦ k, mj = n, and f : I X R → R is continuous. A comparison theorem is employed and the method requires that the Green's function of an associated BVP satisfies certain sign conditions.

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 The Solvability of First Type Boundary Value Problem for a Schrödinger Equation

2020 ◽  
Vol 5 (1) ◽  
pp. 211-220
Author(s):  
Nigar Yildirim Aksoy
Keyword(s):  
Schrödinger Equation ◽  
Boundary Value Problem ◽  
Existence And Uniqueness ◽  
Schrodinger Equation ◽  
Boundary Value ◽  
A Priori ◽  
A Priori Estimate ◽  
Uniqueness Theorems ◽  
Priori Estimate ◽  
Type Boundary

AbstractThe paper presents an first type boundary value problem for a Schrödinger equation. The aim of paper is to give the existence and uniqueness theorems of the boundary value problem using Galerkin’s method. Also, a priori estimate for its solution is given.

scholarly journals On One Interpolation Type Fractional Boundary-Value Problem

Axioms ◽  
2020 ◽  
Vol 9 (1) ◽  
pp. 13 ◽  
Author(s):  
Kateryna Marynets
Keyword(s):  
Differential Equations ◽  
Boundary Value Problem ◽  
Fractional Differential Equations ◽  
Boundary Value ◽  
Approximate Solutions ◽  
Analytic Method ◽  
Fractional Boundary Value Problem ◽  
Mixed Order ◽  
Fractional Differential ◽  
Type Boundary

We present some new results on the approximation of solutions of a special type of fractional boundary-value problem. The focus of our research is a system of three fractional differential equations of the mixed order, subjected to the so-called “interpolation” type boundary restrictions. Under certain conditions, the aforementioned problem is simplified via a proper parametrization technique, and with the help of the numerical-analytic method, the approximate solutions are constructed.

scholarly journals The solution to the Lamb’s problem for nonlocal thermo-visco-elastic medium

2017 ◽  
Vol 66 (4) ◽  
pp. 241-251
Author(s):  
Jerzy August Gawinecki ◽  
Józef Rafa ◽  
Jarosław Łazuka
Keyword(s):  
Differential Equations ◽  
Boundary Value Problem ◽  
Elastic Medium ◽  
Half Space ◽  
Boundary Value ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Biot Model ◽  
Lamb’S Problem ◽  
Initial Boundary Value

In our work we constructed the solution of the initial-boundary value problem so-called Lamb’s problem for the half space occupied with thermo-visco-elastic medium. The visco-elastic medium was described by the Biot model, where as interactions were described by the Gurtin and Pipkin model. Using the Cagniard de Hoop method we obtained the solution of the Lamb’s problem to the considered system of integro-differential equations. Based on the constructed solution of the above mentioned problem, we described the type of waves which propagate in the thermo-visco-elastic medium and the domain of their influence. The propagation of the Rayleigh’s wave was investigated. We discovered the new Rayleigh’s wave in thermo-visco-elastic medium (second Rayleigh’s wave) and named it GRL-wave (Gawinecki-Rafa-Lazuka – wave). Keywords: Lamb’s problem, Danilovskaya’s problem, thermo-visco-elastic medium, Rayleigh’s wave.

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