One Method for the Nonlocal Stabilization of a Burgers-Type Equation by an Impulse Control

Resumo

We study the nonlocal stabilization problem for a hydrodynamic type equation (more precisely, the differentiated Burgers equation) with periodic boundary conditions. The method is based on results in earlier papers, where nonlocal stabilization theory was constructed for a normal semilinear equation obtained from the original differentiated Burgers equation by removing part of the nonlinear terms. In the present paper, nonlocal stabilization of the full original equation by an impulse feedback control is considered. In the future, we intend to extend the results to the 3D Helmholtz equation.