Simultaneous recoveries for semilinear parabolic systems. (1st November 2022)

• Record Type: Journal Article
• Authors: Lin, Yi-Hsuan; Liu, Hongyu; Liu, Xu; Zhang, Shen
• Is Part Of: Inverse problems. Volume 38:Number 11(2022)
• Publication Date: 2022-11-01
• Subjects: inverse boundary problem -- semilinear parabolic equation -- passive measurement -- active measurement -- Carleman estimate -- simultaneous recovery -- uniqueness; Inverse problems (Differential equations) -- Periodicals; 515.357
• DOI: 10.1088/1361-6420/ac91ee
• Languages: English
• ISSNs: 0266-5611

Abstract

Abstract: In this paper, we study inverse boundary problems associated with semilinear parabolic systems in several scenarios where both the nonlinearities and the initial data can be unknown. We establish several simultaneous recovery results showing that the passive or active boundary Dirichlet-to-Neumann operators can uniquely recover both of the unknowns, even stably in a certain case. It turns out that the nonlinearities play a critical role in deriving these recovery results. If the nonlinear term belongs to a general C 1 class but fulfilling a certain growth condition, the recovery results are established by the control approach via Carleman estimates. If the nonlinear term belongs to an analytic class, the recovery results are established through successive linearization in combination with special complex geometrical optics solutions for the parabolic system.