scholarly journals A Mixture Theory for Micropolar Thermoelastic Solids

2007 ◽  
Vol 2007 ◽  
pp. 1-21 ◽  
Author(s):  
C. Galeş
Keyword(s):  
Boundary Value Problem ◽  
Nonlinear Theory ◽  
Mixture Theory ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Uniqueness Result ◽  
Lagrangian Description ◽  
Heat Conducting ◽  
Balance Laws ◽  
Initial Boundary Value

We derive a nonlinear theory of heat-conducting micropolar mixtures in Lagrangian description. The kinematics, balance laws, and constitutive equations are examined and utilized to develop a nonlinear theory for binary mixtures of micropolar thermoelastic solids. The initial boundary value problem is formulated. Then, the theory is linearized and a uniqueness result is established.

scholarly journals An extension of Gronwall inequality in the theory of bodies with voids

Open Physics ◽  
2020 ◽  
Vol 18 (1) ◽  
pp. 1161-1167
Author(s):  
Marin Marin ◽  
Praveen Ailawalia ◽  
Ioan Tuns
Keyword(s):  
Boundary Value Problem ◽  
Internal State ◽  
Boundary Value ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Uniqueness Result ◽  
Internal Variables ◽  
State Variables ◽  
Gronwall’S Inequality ◽  
Initial Boundary Value

Abstract In this paper, we obtain a generalization of the Gronwall’s inequality to cover the study of porous elastic media considering their internal state variables. Based on some estimations obtained in three auxiliary results, we use this form of the Gronwall’s inequality to prove the uniqueness of solution for the mixed initial-boundary value problem considered in this context. Thus, we can conclude that even if we take into account the internal variables, this fact does not affect the uniqueness result regarding the solution of the mixed initial-boundary value problem in this context.

scholarly journals Filtration of Liquid in a Non-isothermal Viscous Porous Medium

2020 ◽  
pp. 763-773
Author(s):  
Alexander A. Papin ◽  
Margarita A. Tokareva ◽  
Rudolf A. Virts
Keyword(s):  
Porous Medium ◽  
Boundary Value Problem ◽  
Fluid Motion ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Heat Conducting ◽  
System Of Equations ◽  
One Dimensional ◽  
Unsteady Fluid ◽  
Initial Boundary Value

The solvability of the initial-boundary value problem is proved for the system of equations of one-dimensional unsteady fluid motion in a heat-conducting viscous porous medium

Definitions of solutions to the IBVP for multi-dimensional scalar balance laws

2018 ◽  
Vol 15 (02) ◽  
pp. 349-374 ◽  
Author(s):  
Elena Rossi
Keyword(s):  
Boundary Value Problem ◽  
Boundary Conditions ◽  
General Framework ◽  
Boundary Value ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Balance Laws ◽  
Initial Boundary Value

We consider four definitions of solution to the initial-boundary value problem (IBVP) for a scalar balance laws in several space dimensions. These definitions are extended to the same most general framework and then compared. The first aim of this paper is to detail differences and analogies among them. We focus then on the ways the boundary conditions are fulfilled according to each definition, providing also connections among these various modes. The main result is the proof of the equivalence among the presented definitions of solution.

The initial–boundary-value problem for real viscous heat-conducting flow with shear viscosity

2003 ◽  
Vol 133 (4) ◽  
pp. 969-986 ◽  
Author(s):  
Dehua Wang
Keyword(s):  
Initial Data ◽  
Boundary Value Problem ◽  
Shear Viscosity ◽  
Boundary Value ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Heat Conducting ◽  
Large Initial Data ◽  
Viscous Heat ◽  
Initial Boundary Value

An initial–boundary-value problem for the nonlinear equations of real compressible viscous heat-conducting flow with general large initial data is investigated. The main point is to study the real flow for which the pressure and internal energy have nonlinear dependence on temperature, unlike the linear dependence for ideal flow, and the viscosity coefficients and heat conductivity are also functions of density and/or temperature. The shear viscosity is also presented. The existence, uniqueness and regularity of global solutions are established with large initial data in H1. It is shown that there is no shock wave, vacuum, mass concentration, or heat concentration (hot spots) developed in a finite time, although the solutions have large oscillations.

scholarly journals Initial Boundary Value Problem of the General Three-Component Camassa-Holm Shallow Water System on an Interval

2013 ◽  
Vol 2013 ◽  
pp. 1-15
Author(s):  
Lixin Tian ◽  
Qingwen Yuan ◽  
Lizhen Wang
Keyword(s):  
Boundary Value Problem ◽  
Shallow Water ◽  
Blow Up ◽  
Boundary Value ◽  
Water System ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Uniqueness Result ◽  
Shallow Water System ◽  
Initial Boundary Value

We study the initial boundary value problem of the general three-component Camassa-Holm shallow water system on an interval subject to inhomogeneous boundary conditions. First we prove a local in time existence theorem and present a weak-strong uniqueness result. Then, we establish a asymptotic stabilization of this system by a boundary feedback. Finally, we obtain a result of blow-up solution with certain initial data and boundary profiles.

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