Inverse Problems for Single and Strongly Coupled PDEs via Boundary Measurements: a Carleman Estimates Approach

2011 ◽  
Author(s):  
Shitao Liu
Keyword(s):  
Inverse Problems ◽  
Carleman Estimates ◽  
Strongly Coupled ◽  
Boundary Measurements

scholarly journals Stability estimate for a strongly coupled parabolic system

2012 ◽  
Vol 43 (1) ◽  
pp. 137-144 ◽  
Author(s):  
Kun-Chu Chen
Keyword(s):  
Parabolic System ◽  
Stability Estimate ◽  
Carleman Estimates ◽  
Inverse Source Problem ◽  
Lipschitz Stability ◽  
Strongly Coupled

We consider an inverse source problem for a 2×2 strongly coupled parabolic system. The Lipschitz stability is proved and the proof is based on the Carleman estimates with two large parameters.

Inverse Problems and Carleman Estimates

2021 ◽  
Author(s):  
Michael V. Klibanov ◽  
Jingzhi Li
Keyword(s):  
Inverse Problems ◽  
Carleman Estimates

Inverse problems for linear degenerate parabolic equations by “time-like” Carleman estimate

2015 ◽  
Vol 23 (1) ◽  
pp. 1-21 ◽  
Author(s):  
Atsushi Kawamoto
Keyword(s):  
Inverse Problems ◽  
Parabolic Equations ◽  
Fixed Time ◽  
Carleman Estimate ◽  
Coupled Systems ◽  
Degenerate Parabolic Equations ◽  
Strongly Coupled ◽  
Degenerate Parabolic ◽  
Inverse Source Problems ◽  
Linear Degenerate

AbstractIn this paper, we study inverse problems for multi-dimensional linear degenerate parabolic equations and strongly coupled systems. In particular we discuss the Lipschitz type stability results for the inverse source problems which determine a source term by boundary data on an appropriate sub-boundary and the data on any fixed time. Our arguments are based on the Carleman estimate. Here we prove and use the Carleman estimate with the

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