scholarly journals Three-Dimensional Generalized Dynamics of Soft-Matter Quasicrystals

2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Tian-You Fan ◽  
Zhi-Yi Tang
Keyword(s):  
Boundary Value Problems ◽  
Soft Matter ◽  
Boundary Value ◽  
Three Dimensional ◽  
Governing Equations

The three-dimensional generalized dynamics of soft-matter quasicrystals was investigated, in which the governing equations of the dynamics are derived for observed 12-fold symmetry quasicrystals and possibly observed 8- and 10-fold symmetry ones in soft matter. The solving methods, possible solutions for some initial- and boundary-value problems of the equations, and possible applications are discussed as well.

scholarly journals Initial boundary value problems for the three-dimensional compressible elastic Navier-Stokes-Poisson equations

2021 ◽  
Vol 10 (1) ◽  
pp. 1356-1383
Author(s):  
Yong Wang ◽  
Wenpei Wu
Keyword(s):  
Equilibrium State ◽  
Boundary Value Problems ◽  
Electrostatic Potential ◽  
Boundary Value ◽  
Three Dimensional ◽  
Initial Boundary ◽  
Navier Stokes ◽  
Initial Boundary Value Problems ◽  
Poisson Equations ◽  
Initial Boundary Value

Abstract We study the initial-boundary value problems of the three-dimensional compressible elastic Navier-Stokes-Poisson equations under the Dirichlet or Neumann boundary condition for the electrostatic potential. The unique global solution near a constant equilibrium state in H 2 space is obtained. Moreover, we prove that the solution decays to the equilibrium state at an exponential rate as time tends to infinity. This is the first result for the three-dimensional elastic Navier-Stokes-Poisson equations under various boundary conditions for the electrostatic potential.

Basic Boundary Value Problems of Thermoelasticity for Anisotropic Bodies with Cuts. I

1995 ◽  
Vol 2 (2) ◽  
pp. 123-140
Author(s):  
R. Duduchava ◽  
D. Natroshvili ◽  
E. Shargorodsky
Keyword(s):  
Boundary Value Problems ◽  
Displacement Vector ◽  
Boundary Value ◽  
Three Dimensional ◽  
Manifolds With Boundary ◽  
Hölder Continuous ◽  
Arbitrary Configuration ◽  
Anisotropic Bodies ◽  
Potential Methods ◽  
Basic Boundary

Abstract The three-dimensional problems of the mathematical theory of thermoelasticity are considered for homogeneous anisotropic bodies with cuts. It is assumed that the two-dimensional surface of a cut is a smooth manifold of an arbitrary configuration with a smooth boundary. The existence and uniqueness theorems for boundary value problems of statics and pseudo-oscillations are proved in the Besov and Bessel-potential spaces by means of the classical potential methods and the theory of pseudodifferential equations on manifolds with boundary. Using the embedding theorems, it is proved that the solutions of the considered problems are Hölder continuous. It is shown that the displacement vector and the temperature distribution function are Cα -regular with any exponent α < 1/2. This paper consists of two parts. In this part all the principal results are formulated. The forthcoming second part will deal with the auxiliary results and proofs.

Solutions to Particular Three-Dimensional Boundary Value Problems of Elastostatics

2013 ◽  
pp. 209-218
Author(s):  
Reza Eslami ◽  
Richard B. Hetnarski ◽  
Jozef Ignaczak ◽  
Naotake Noda ◽  
Naobumi Sumi ◽  
...  
Keyword(s):  
Boundary Value Problems ◽  
Boundary Value ◽  
Three Dimensional ◽  
Dimensional Boundary

scholarly journals On the Modeling of Five-Layer Thin Prismatic Bodies

2019 ◽  
Vol 24 (3) ◽  
pp. 69 ◽  
Author(s):  
Mikhail U. Nikabadze ◽  
Armine R. Ulukhanyan ◽  
Tamar Moseshvili ◽  
Ketevan Tskhakaia ◽  
Nodar Mardaleishvili ◽  
...  
Keyword(s):  
Orthogonal Polynomials ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
Three Dimensional ◽  
Initial Boundary ◽  
Initial Boundary Value Problems ◽  
Micropolar Theory ◽  
Prismatic Bodies ◽  
Initial Boundary Value

Proceeding from three-dimensional formulations of initial boundary value problems of the three-dimensional linear micropolar theory of thermoelasticity, similar formulations of initial boundary value problems for the theory of multilayer thermoelastic thin bodies are obtained. The initial boundary value problems for thin bodies are also obtained in the moments with respect to systems of orthogonal polynomials. We consider some particular cases of formulations of initial boundary value problems. In particular, the statements of the initial-boundary value problems of the micropolar theory of K-layer thin prismatic bodies are considered. From here, we can easily get the statements of the initial-boundary value problems for the five-layer thin prismatic bodies.

Sign in / Sign up

Export Citation Format

Share Document