Stabilization of the wave equation with boundary or internal distributed delay. (English) Zbl 1224.35247

Nicaise, Serge; Pignotti, Cristina

Differ. Integral Equ. 21, No. 9-10, 935-958 (2008).

Summary: We consider the wave equation in a bounded region with a smooth boundary with distributed delay on the boundary or into the domain. In both cases, under suitable assumptions, we prove the exponential stability of the solution. These results are obtained by introducing suitable energies and by proving some observability inequalities. For an internal distributed delay, we further show some instability results.

MSC:

35L05	Wave equation
35L20	Initial-boundary value problems for second-order hyperbolic equations
93D15	Stabilization of systems by feedback

Keywords:

wave equation; exponential stability; internal distributed delay