Simultaneous Identification of Damping Coefficient and Initial Value in PDEs from boundary measurement

2016/05/17 by Zhi-Xue Zhao, Zhao, Zhi-Xue, Mapundi K. Banda +3
Engineering · Mathematics · Physics and Astronomy · #35R30 #65M32 #65N21 #93B30 #Analysis of PDEs (math.AP) #FOS: Mathematics #Model Reduction and Neural Networks #Numerical methods in inverse problems #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.1605.05063

openalex publication_date 2016/05/17 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

In this paper, the simultaneous identification of damping or anti-damping coefficient and initial value for some PDEs is considered. An identification algorithm is proposed based on the fact that the output of 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.

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