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

Large time behavior of differential equations with drifted periodic coefficients modeling Carbon storage in soil

This paper is concerned with the linear ODE in the form $y'(t)=\lambda\rho(t)y(t)+b(t)$, $\lambda <0$ which represents a simplified storage model of the carbon in the soil. In the first part, we show that, for a periodic function $\rho(t)$, a linear drift in the coefficient $b(t)$ involves a linear drift for the solution of this ODE. In the second part, we extend the previous results to a classical heat non-homogeneous equation. The connection with an analytic semi-group associated to the ODE equation is considered in the third part. Numerical examples are given.Comment: 18 page

Determine the source term of a two-dimensional heat equation

Let $\Omega$ be a two-dimensional heat conduction body. We consider the problem of determining the heat source $F(x,t)=\varphi(t)f(x,y)$ with $\varphi$ be given inexactly and $f$ be unknown. The problem is nonlinear and ill-posed. By a specific form of Fourier transforms, we shall show that the heat source is determined uniquely by the minimum boundary condition and the temperature distribution in $\Omega$ at the initial time $t=0$ and at the final time $t=1$. Using the methods of Tikhonov's regularization and truncated integration, we construct the regularized solutions. Numerical part is given.Comment: 18 page

Determination of the body force of a two-dimensional isotropic elastic body

Let $\Omega$ represent a two$-$dimensional isotropic elastic body. We consider the problem of determining the body force $F$ whose form $\phi(t)(f_1(x),f_2(x))$ with $\phi$ be given inexactly. The problem is nonlinear and ill-posed. Using the Fourier transform, the methods of Tikhonov's regularization and truncated integration, we construct a regularized solution from the data given inexactly and derive the explicitly error estimate. Numerical part is givenComment: 23 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

Studying livestock breeding wastewater treatment with bentonite adsorbent

The possibility of using adsorbents (bentonite, diatomite and kaolinite) for obtaining adsorptive materials effective in livestock breeding wastewater treatment has been assessed. It has been shown on the example of ions of ammonia (NH4) and phosphate (PO43) that particles of bentonite have relatively high adsorption capacity. The data about adsorption kinetics have been processed with the use of first and second-order kinetic models. It has been revealed that the second-order kinetic model described better adsorption of ammonia and phosphate from aqueous solutions by particles of bentonit

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

A Hybrid of Adaptation and Dynamic Routing based on SDN for Improving QoE in HTTP Adaptive VBR Video Streaming

Recently, HTTP Adaptive Streaming HAS has received significant attention from both industry and academia based on its ability to enhancing media streaming services over the Internet. Recent research solutions that have tried to improve HAS by adaptation at the client side only may not be completely effective without interacting with routing decisions in the upper layers. In this paper, we address the aforementioned issue by proposing a dynamic bandwidth allocation and management architecture for streaming video flows to improve users satisfaction. We also introduce an initial cross layer hybrid method that combines quality adaptation of variable bitrate video streaming over the HTTP protocol at the client side and SDN based dynamical routing. This scheme is enabled by the Software Defined Networking architecture that is now being considered as an emerging paradigm that disassociates the forwarding process from the routing process. SDN brings flexibility and the ability to flexibly change routing solutions, in turn resulting in dynamically improving the services provided in the application layer. Our experimental results show that the proposed solution offers significantly higher overall bitrates as well as smoother viewing experience than existing methods.Comment: 14 pages, 17 figures, IJCSNS International Journal of Computer Science and Network Security, http://paper.ijcsns.org/07_book/201907/20190708.pd