Journal
JOURNAL OF DIFFERENTIAL EQUATIONS
Volume 305, Issue -, Pages 45-71Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jde.2021.10.007
Keywords
Inverse problems; First-order hyperbolic equations; Carleman estimates; Integral curves; Characteristic curves
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Funding
- Istituto Nazionale di Alta Matematica (INdeltaAM)
- [JP20J11497]
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The study proves global Lipschitz stability for inverse source and coefficient problems of first-order linear hyperbolic equations, where the key lies in choosing the length of integral curves to construct a weight function for the Carleman estimate. These integral curves correspond to characteristic curves in certain cases.
We prove global Lipschitz stability for inverse source and coefficient problems for first-order linear hyperbolic equations, the coefficients of which depend on both space and time. We use a global Carleman estimate, and a crucial point, introduced in this paper, is the choice of the length of integral curves of a vector field generated by the principal part of the hyperbolic operator to construct a weight function for the Carleman estimate. These integral curves correspond to the characteristic curves in some cases. (c) 2021 Elsevier Inc. All rights reserved.
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