This work is devoted to discussing that how the locations of the thermal and viscous damping affect the stability of the 1-d elastic systems. The spatial domain of the 1-d thermoelastic system under consideration can be divided into three sub -intervals, that is, the thermoelastic region of type II, the one of type II with viscous damping, and the one of type III. The following two kinds of energy decay rates for the system are obtained: 1. If the thermoelastic region of type III includes one exterior point of the spatial domain of the system, the energy of the system decays exponentially; 2. If not, that is the thermoelastic region of type III is strictly inside the spatial domain, the system always lacks of exponential decay. However, the optimal polynomial decay rate is further estimated for this system with smooth initial states. Finally, some numerical simulations are presented to verify the stability results obtained in this work. (C) 2019 Elsevier Inc. All rights reserved.

We consider a one-dimensional radiation hydrodynamics model in the case of the equilibrium diffusion approximation which is described by the compressible Navier-Stokes system with the additional terms in the pressure and internal energy respectively, which embody the effect of radiation. Under the physical growth conditions on the heat conductivity, we establish the existence and uniqueness of strong solutions to the Cauchy problem with large initial data, where the initial density and velocity may have differing constant states at infinity. Moreover, we show that if there is no vacuum ill the initial density, then, the vacuum and concentration of the density will never occur in any finite time. (C) 2008 Elsevier Inc. All rights reserved.

This paper presents the exponential stability of a one-dimensional wave equation with viscoelastic damping. Using the asymptotic analysis technique, we prove that the spectrum of the system operator consists of two parts: the point and continuous spectrum. The continuous spectrum is a set of N points which are the limits of the eigenvalues of the system, and the point spectrum is a set of three classes of eigenvalues: one is a subset of N isolated simple points, the second is approaching to a vertical line which parallels to the imagine axis, and the third class is distributed around the continuous spectrum. Moreover, the Riesz basis property of the generalized eigenfunctions of the system is verified. Consequently, the spectrum-determined growth condition holds true and the exponential stability of the system is then established. (C) 2013 Elsevier Inc. All rights reserved.

In this paper we study the asymptotic limiting behavior of the solutions to the initial boundary value problem for linearized one-dimensional compressible Navier-Stokes equations. We consider the characteristic boundary conditions, that is we assume that an eigenvalue of the associated inviscid Euler system vanishes uniformly on the boundary. The aim of this paper is to understand the evolution of the boundary layer, to construct the asymptotic ansatz which is uniformly valid up to the boundary, and to obtain rigorously the uniform convergence to the solution of the Euler equations without the weakness assumption on the boundary layer. (C) 2010 Elsevier Inc. All rights reserved.

A parabolic system with small viscosity is considered in a two dimensional channel. With the help of discussions on suitable boundary conditions of the corresponding hyperbolic equations on both sides of the channel, the existence and stability of multiple boundary layers are proved by using the matched asymptotic analysis and energy estimates. The results therefore consequently justify the zero viscosity limit when epsilon tends to 0. (C) 2015 Elsevier Inc. All rights reserved.