Abstract
In this paper, we study the Lipschitz stability in inverse source problems for degenerate/singular parabolic equations in the case of a boundary observation. First, we establish new global Carleman estimates, which improve that derived by Vancostenoble (2011). Then, following the general lines of the approach introduced by Imanuvilov and Yamamoto (1998), we prove the Lipschitz stability in the inverse source problems. The results obtained are natural extensions of many previous results for parabolic equations without/with degeneracy or singularity.
Acknowledgements
The authors would like to thank the reviewers for the helpful comments and suggestions, which helped to improve the presentation of the paper. The authors would like to thank Hanoi National University of Education for providing a fruitful working environment.
References
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© 2022 Walter de Gruyter GmbH, Berlin/Boston
Artikel in diesem Heft
- Frontmatter
- Lipschitz stability in inverse source problems for degenerate/singular parabolic equations by the Carleman estimate
- The asymptotic behavior of the solution of an inverse problem for the pseudoparabolic equation
- On uniqueness and nonuniqueness for internal potential reconstruction in quantum fields from one measurement II. The non-radial case
- Adaptive Runge–Kutta regularization for a Cauchy problem of a modified Helmholtz equation
- On finding a penetrable obstacle using a single electromagnetic wave in the time domain
- Direct and inverse problems for time-fractional heat equation generated by Dunkl operator
- Agent-based mathematical model of COVID-19 spread in Novosibirsk region: Identifiability, optimization and forecasting
- Certain inverse uniqueness from the quotients of scattering coefficients
- On recovery of an unbounded bi-periodic interface for the inverse fluid-solid interaction scattering problem
- Approximate Lipschitz stability for phaseless inverse scattering with background information
- The mean field games system: Carleman estimates, Lipschitz stability and uniqueness
Artikel in diesem Heft
- Frontmatter
- Lipschitz stability in inverse source problems for degenerate/singular parabolic equations by the Carleman estimate
- The asymptotic behavior of the solution of an inverse problem for the pseudoparabolic equation
- On uniqueness and nonuniqueness for internal potential reconstruction in quantum fields from one measurement II. The non-radial case
- Adaptive Runge–Kutta regularization for a Cauchy problem of a modified Helmholtz equation
- On finding a penetrable obstacle using a single electromagnetic wave in the time domain
- Direct and inverse problems for time-fractional heat equation generated by Dunkl operator
- Agent-based mathematical model of COVID-19 spread in Novosibirsk region: Identifiability, optimization and forecasting
- Certain inverse uniqueness from the quotients of scattering coefficients
- On recovery of an unbounded bi-periodic interface for the inverse fluid-solid interaction scattering problem
- Approximate Lipschitz stability for phaseless inverse scattering with background information
- The mean field games system: Carleman estimates, Lipschitz stability and uniqueness