The regularity and exponential decay of solution for a linear wave equation associated with two-point boundary conditions

This paper is concerned with the existence and the regularity of global solutions to the linear wave equation associated with two-point type boundary conditions. We also investigate the decay properties of the global solutions to this problem by the construction of a suitable Lyapunov functional.Comment: 18 page

Existence, blow-up and exponential decay estimates for a nonlinear wave equation with boundary conditions of two-point type

This paper is devoted to study a nonlinear wave equation with boundary conditions of two-point type. First, we state two local existence theorems and under suitable conditions, we prove that any weak solutions with negative initial energy will blow up in finite time. Next, we give a sufficient condition to guarantee the global existence and exponential decay of weak solutions. Finally, we present numerical resultsComment: 2

University Students' Perceptions of Native and Non-Native English-Speaking Teachers in Pre-Sessional Courses in Vietnam

Research Articl

On a nonlinear heat equation associated with Dirichlet -- Robin conditions

This paper is devoted to the study of a nonlinear heat equation associated with Dirichlet-Robin conditions. At first, we use the Faedo -- Galerkin and the compactness method to prove existence and uniqueness results. Next, we consider the properties of solutions. We obtain that if the initial condition is bounded then so is the solution and we also get asymptotic behavior of solutions as. Finally, we give numerical resultsComment: 20 page

Existence and Decay of Solutions of a Nonlinear Viscoelastic Problem with a Mixed Nonhomogeneous Condition

We study the initial-boundary value problem for a nonlinear wave equation given by u_{tt}-u_{xx}+\int_{0}^{t}k(t-s)u_{xx}(s)ds+ u_{t}^{q-2}u_{t}=f(x,t,u) , 0 < x < 1, 0 < t < T, u_{x}(0,t)=u(0,t), u_{x}(1,t)+\eta u(1,t)=g(t), u(x,0)=\^u_{0}(x), u_{t}(x,0)={\^u}_{1}(x), where \eta \geq 0, q\geq 2 are given constants {\^u}_{0}, {\^u}_{1}, g, k, f are given functions. In part I under a certain local Lipschitzian condition on f, a global existence and uniqueness theorem is proved. The proof is based on the paper [10] associated to a contraction mapping theorem and standard arguments of density. In Part} 2, under more restrictive conditions it is proved that the solution u(t) and its derivative u_{x}(t) decay exponentially to 0 as t tends to infinity.Comment: 26 page

THE UNIFORM EXPONENTIAL STABILITY OF LINEAR SKEW-PRODUCT SEMIFLOWS ON REAL HILBERT SPACE

The goal of the paper is to present some characterizations for the uniform exponential stability of linear skew-product semiflows on real Hilbert space

Effects of bribery on natural resource efficiency in Vietnam: moderating effects of market competition and credit constraints

This article uses small and medium-sized enterprises’ (SMEs) survey data in Vietnam from 2007 to 2015 to examine the effects of bribery on the natural resource efficiency of firms facing credit constraints and market competition. We also employ the disaggregated resource intensity by water, fuel, and electricity. Creditconstrained firms are broken down into those who have had formal loan applications denied (credit rationed) and those who do not apply for formal loans due to either the process being too difficult or the interest rate being too high (discouraged borrowers). Applying instrumental variable method to take into account the endogeneity problem, the empirical results provide evidence to support the ‘sanding-the-wheels of resource efficiency’ hypothesis. Among the three natural resources, inefficiency is most evident in water consumption. Furthermore, the effects become more sizable for micro-sized and informally registered firms since they have a lower bargaining power vis-a-vis public officials. Credit constraints and market competition pressure can reduce a firm’s ability to use natural resources efficientl