Well-posedness Analysis Of Neural Network And Stabilization Of Wave Equation With Distributed Disturbance

Since the 1980 s, the partial differential network by its rich application background has been the attention of many scholars. From the classical natural science(for example,population biology, medicine and electronic informatics, etc.) to the social sciences(such as demographic and management, etc.), from the network structure of the model to the network structure of the dynamic behavior of the physical, biological, or society. More and more partial differential network(such as elasticity, heat conduction network, flow network and the neural network, etc.) into the research category of people, with the progress of science and technology and the development of society, network problems there will be more broad application prospects.In this paper, we consider neural network. Firstly, based on the past research of neural network model, we improve the existing FitzHugh–Nagumo-Rall model, and prove that the new model is interior well-posed by using the semigroups of operators. Then, we study the stabilization problem of a one-dimensional wave equation with unknown disturbance. In order to stabilize the system with disturbance, we design a distributed feedback controller by employing the idea of sliding mode control technology. For the resulted nonlinear closedloop system, we prove its solvability by using the maximal monotone operator. Further we prove the exponentially stable of the closed-loop system. Finally, we verify the effectiveness of the proposed controller by using Matlab Numerical simulation.