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

DETERMINATION OF THE PLANT LOCATIONS FOR ENSURING SOME ENVIRONMENTAL CRITERIA

Joint Research on Environmental Science and Technology for the Eart

DETERMINATION OF THE PLANT LOCATIONS FOR ENSURING SOME ENVIRONMENTAL CRITERIA

Joint Research on Environmental Science and Technology for the Eart

Determine the spacial term of a two-dimensional heat source

We consider the problem of determining a pair of functions $(u,f)$ satisfying the heat equation $u_t -\Delta u =\varphi(t)f (x,y)$, where $(x,y)\in \Omega=(0,1)\times (0,1)$ and the function $\varphi$ is given. The problem is ill-posed. Under a slight condition on $\varphi$, we show that the solution is determined uniquely from some boundary data and the initial temperature. Using the interpolation method and the truncated Fourier series, we construct a regularized solution of the source term $f$ from non-smooth data. The error estimate and numerical experiments are given.Comment: 18 page

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

A fundamental study on mangrove plantation at mud flats

Joint Research on Environmental Science and Technology for the Eart