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

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

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

Model Updating for Large-Scale Railway Bridge Using Grey Wolf Algorithm and Genetic Alghorithms

This paper proposes a novel hybrid algorithm to deal with an inverse problem of a large-scale truss bridge. Grey Wolf Optimization (GWO) Algorithm is a well-known and widely applied metaheuristic algorithm. Nevertheless, GWO has two major drawbacks. First, this algorithm depends crucially on the positions of the leading Wolf. If the position of the leaderis far from the best solution, the obtained results are poor. On the other hand, GWO does not own capacities to improve the quality of new generations if elements are trapped into local minima. To remedy the shortcomings of GWO, we propose a hybrid algorithm combining GWO with Genetic Algorithm (GA), termed HGWO-GA. This proposed method contains two key features (1) based on crossover and mutation capacities, GA is first utilized to generate the high-quality elements (2) after that, the optimization capacity of GWO is employed to seek the optimal solutions. To assess the effectiveness of the proposed approach, a large-scale truss bridge is employed for model updating. The obtained results show that HGWO-GA not only provides a good agreement between numerical and experimental results but also outperforms traditional GWO in terms of accuracy

The effect of metal corrosion on the structural reliability of the Pre-Engineered steel frame

Nowadays, Pre-Engineered steel buildings are widely used in the field of the industrial construction. However, design standards often only care about the safety (or reliability) at the start time but not concerned about the deterioration of reliability during used under the metal corrosive of environment. Meanwhile, reliability and durability of steel structure depend heavily on metal corrosion of environmental, this is uncertainty parameters. In this research presents the effect of the safety of Pre-Engineered steel frames considering metal corrosion. The metal corrosion modeling used to propose by M.E. Komp. Reliability of the structure is evaluated using Monte Carlo simulation method and Finite Element Method (FEM). This computer program is written by using the MATLAB programming language. The results numbers are reliability and durability behaviors under corrosion are determined for exposure about from 10 - 50 years. Effects of input parameters are also investigated