Simultaneous identification of damping coefficient and initial value for PDEs from boundary measurement

Abstract

In this paper, simultaneous identification of damping or anti-damping coefficient and initial value for some Riesz spectral systems is considered. An identification algorithm is proposed based on the fact that the output of the system happens to be decomposed into a product of an exponential function and a periodic function. The former contains information of the damping coefficient, while the latter does not. The convergence and error analysis are also developed. Three examples, namely an anti-stable wave equation with boundary anti-damping, the Schrödinger equation with internal anti-damping and two connected strings with middle joint anti-damping, are investigated and demonstrated by numerical simulations to show the effectiveness of the proposed algorithm.