Stability Of Wave Systems With Acoustic Boundary Conditions For A Non-locally Reacting Boundary With Delays Disturbance

The wave system with non-local response acoustic boundary conditions is an important class of nonlinear partial differential equations.This type of model is mostly used for noise control and suppression in practical application research.Therefore,studying the control problems of such models has important practical value and theoretical significance.Among them,the research on the uniform stability of the PDE system is an important research direction in this distributed parameter system control research.In the second chapter,we study the uniform stability of a wave system with nonlocal reactive acoustic boundary conditions under internal time-delay perturbations.Finally,the general decay rate of the energy of the corresponding nonlinear system is obtained by using the multiplier method and the scaling technique of inequality.For some boundary terms,we use the truncation function.In the third chapter,we study the uniform stability of wave systems with nonlocal acoustic boundary conditions under boundary time-delay perturbations.The difference from the second chapter is that for the treatment of tangent derivative terms,we use lemma 7.2 in lasiecka and tartaru [29],Finally,the general energy decay rate of the corresponding nonlinear system is obtained by the multiplier method and the scaling technique of inequality.