Well‐posedness and stability of a nonlinear time‐delayed dispersive equation via the fixed point technique: A case study of no interior damping

Abstract

The primary concern of this article is to establish the well‐posedness as well as the exponential stability of the zero solution to a nonlinear time‐delayed dispersive equation of order four in a bounded interval. The main ingredient of the proof is the exploitation of Schauder Fixed Point Theorem. This outcome considerably improves an earlier result of Ammari et al. (2021) in the sense that we prove that no interior damping control is required. Furthermore, our results remain valid regardless of the sign of the antidiffusion parameter. Numerical simulations are also given as an illustration of our theoretical result.

Stability of Sensor Network based on Non-linear Data Analysis for in situ Leaching of Ionic Rare Earth Ore Bodies under Similar Simulation Experiments

“…The data are transmitted quickly, the energy consumption is low, and the power consumption is very low. From the analysis and comparison of Table 1, we can see that each wireless SN technology has different characteristics and advantages in different application fields (Ammari et al, 2022;Popkov et al, 2022). The aim of this study was to design and study the monitoring system for the stope slope of RE mines.…”