Recovery of Nonlinear Terms for Reaction Diffusion Equations from Boundary Measurements

In the present article we study the inverse problem of determining a general semilinear term for a class of nonlinear parabolic equations. We derive a new criterion for the unique and stable recovery of general semilinear terms for these type of equations from the knowledge of the parabolic Dirichle...

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Bibliographic Details
Published in:Archive for rational mechanics and analysis 2023-02, Vol.247 (1), p.6, Article 6
Main Authors: Kian, Yavar, Uhlmann, Gunther
Format: Article
Language:English
Subjects:
Boundary value problems
Classical Mechanics
Complex Systems
Digital Object Identifier
Dirichlet problem
Fluid- and Aerodynamics
Inverse problems
Mathematical analysis
Mathematical and Computational Physics
Mathematics
Physics
Physics and Astronomy
Reaction-diffusion equations
Recovery
Theoretical
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Summary:In the present article we study the inverse problem of determining a general semilinear term for a class of nonlinear parabolic equations. We derive a new criterion for the unique and stable recovery of general semilinear terms for these type of equations from the knowledge of the parabolic Dirichlet-to-Neumann map associated with solutions of the equation having zero initial data.
ISSN:0003-9527
1432-0673
DOI:10.1007/s00205-022-01831-y