In this paper, the focus is on the boundary stability of a nanolayer in diffusion-reaction systems, taking into account a nonlinear boundary control condition. The authors focus on demonstrating the boundary stability...In this paper, the focus is on the boundary stability of a nanolayer in diffusion-reaction systems, taking into account a nonlinear boundary control condition. The authors focus on demonstrating the boundary stability of a nanolayer using the Lyapunov function approach, while making certain regularity assumptions and imposing appropriate control conditions. In addition, the stability analysis is extended to more complex systems by studying the limit problem with interface conditions using the epi-convergence approach. The results obtained in this article are then tested numerically to validate the theoretical conclusions.展开更多
After describing a general sampling discretization algorithm for multistage continuous stochastic programming problems, we prove the global convergence of the al- gorithm under suitable conditions. The convergence of ...After describing a general sampling discretization algorithm for multistage continuous stochastic programming problems, we prove the global convergence of the al- gorithm under suitable conditions. The convergence of most available algorithms as well as new algorithms can thus be derived or improved as a special case of this general result.展开更多
文摘In this paper, the focus is on the boundary stability of a nanolayer in diffusion-reaction systems, taking into account a nonlinear boundary control condition. The authors focus on demonstrating the boundary stability of a nanolayer using the Lyapunov function approach, while making certain regularity assumptions and imposing appropriate control conditions. In addition, the stability analysis is extended to more complex systems by studying the limit problem with interface conditions using the epi-convergence approach. The results obtained in this article are then tested numerically to validate the theoretical conclusions.
文摘After describing a general sampling discretization algorithm for multistage continuous stochastic programming problems, we prove the global convergence of the al- gorithm under suitable conditions. The convergence of most available algorithms as well as new algorithms can thus be derived or improved as a special case of this general result.
