Can Nguyen

Bio: Can Nguyen is an academic researcher from Ton Duc Thang University. The author has contributed to research in topics: Well-posed problem & Tikhonov regularization. The author has an hindex of 1, co-authored 1 publications receiving 3 citations.

Identification of source term for the ill-posed Rayleigh–Stokes problem by Tikhonov regularization method

Abstract: In this paper, we study an inverse source problem for the Rayleigh–Stokes problem for a generalized second-grade fluid with a fractional derivative model. The problem is severely ill-posed in the sense of Hadamard. To regularize the unstable solution, we apply the Tikhonov method regularization solution and obtain an a priori error estimate between the exact solution and regularized solutions. We also propose methods for both a priori and a posteriori parameter choice rules. In addition, we verify the proposed regularized methods by numerical experiments to estimate the errors between the regularized and exact solutions.

Use of Neural Network Based Prediction Algorithms for Powering Up Smart Portable Accessories

Abstract: Emerging Trends in the use of smart portable accessories, particularly within the context of the Internet of Things (IoT), where smart sensor devices are employed for data gathering, require advancements in energy management mechanisms. This study aims to provide an intelligent energy management mechanism for wearable/portable devices through the use of predictions, monitoring, and analysis of the performance indicators for energy harvesting, majorly focusing on the hybrid PV-wind systems. To design a robust and precise model, prediction algorithms are compared and analysed for an efficient decision support system. Levenberg–Marquardt (LM), Bayesian Regularization (BR), and Scaled Conjugate Gradient (SCG) prediction algorithms are used to develop a Shallow Neural Network (SNN) for time series prediction. The proposed SNN model uses a closed-loop NARX recurrent dynamic neural network to predict the active power and energy of a hybrid system based on the experimental data of solar irradiation, wind speed, wind direction, humidity, precipitation, ambient temperature and atmospheric pressure collected from Jan 1st 2015 to Dec 26th 2015. The historical hourly metrological data set is established using calibrated sensors deployed at Middle East Technical University (METU), NCC. The accessory considered in this study is called as Smart Umbrella System (SUS), which uses a Raspberry Pi module to fetch the weather data from the current location and store it in the cloud to be processed using SNN classified prediction algorithms. The results obtained show that using the SNN model, it is possible to obtain predictions with 0.004 error rate in a computationally efficient way within 20 s. With the experiments, we are able to observe that for the period of observation, the energy harvested is 178 Wh/d, where the system estimates energy as 176.5 Wh/d, powering the portable accessories accurately.

Backward and Non-Local Problems for the Rayleigh-Stokes Equation

Abstract: This paper presents the method of separation of variables to find conditions on the right-hand side and on the initial data in the Rayleigh-Stokes problem, which ensure the existence and uniqueness of the solution. Further, in the Rayleigh-Stokes problem, instead of the initial condition, the non-local condition is considered: u(x,T)=βu(x,0)+φ(x), where β is equal to zero or one. It is well known that if β=0, then the corresponding problem, called the backward problem, is ill-posed in the sense of Hadamard, i.e., a small change in u(x,T) leads to large changes in the initial data. Nevertheless, we will show that if we consider sufficiently smooth current information, then the solution exists, it is unique and stable. It will also be shown that if β=1, then the corresponding non-local problem is well-posed and inequalities of coercive type are satisfied.

Determine unknown source problem for time fractional pseudo-parabolic equation with Atangana-Baleanu Caputo fractional derivative

Abstract: In this paper, we consider a pseudo-parabolic equation with the Atangana-Baleanu Caputo fractional derivative. Our main tool here is using fundamental tools, namely the Fractional Tikhonov method and the generalized Tikhonov method, the error estimate is shown. Finally, we provided numerical experiments to prove the correctness of our theory.

A Non-Local Problem for the Fractional-Order Rayleigh–Stokes Equation

Abstract: A nonlocal boundary value problem for the fractional version of the Rayleigh–Stokes equation, well-known in fluid dynamics, is studied. Namely, the condition u(x,T)=βu(x,0)+φ(x), where β is an arbitrary real number, is proposed instead of the initial condition. If β=0, then we have the inverse problem in time, called the backward problem. It is well-known that the backward problem is ill-posed in the sense of Hadamard. If β=1, then the corresponding non-local problem becomes well-posed in the sense of Hadamard, and moreover, in this case a coercive estimate for the solution can be established. The aim of this work is to find values of the parameter β, which separates two types of behavior of the semi-backward problem under consideration. We prove the following statements: if β≥1, or β<0, then the problem is well-posed; if β∈(0,1), then depending on the eigenvalues of the elliptic part of the equation, for the existence of a solution an additional condition on orthogonality of the right-hand side of the equation and the boundary function to some eigenfunctions of the corresponding elliptic operator may emerge.