scholarly journals Stability for inverse source problems by Carleman estimates

2020 ◽  
Vol 36 (12) ◽  
pp. 125006
Author(s):  
X Huang ◽  
O Yu Imanuvilov ◽  
M Yamamoto
Keyword(s):  
Carleman Estimates ◽  
Inverse Source Problems

Lipschitz stability estimates in inverse source problems for a fractional diffusion equation of half order in time by Carleman estimates

2018 ◽  
Vol 26 (5) ◽  
pp. 647-672 ◽  
Author(s):  
Atsushi Kawamoto
Keyword(s):  
Diffusion Equation ◽  
Additional Data ◽  
Fixed Time ◽  
Fractional Diffusion ◽  
Fractional Diffusion Equation ◽  
Carleman Estimates ◽  
Time Interval ◽  
Stability Estimates ◽  
Lipschitz Stability ◽  
Inverse Source Problems

Abstract In this article, we consider a fractional diffusion equation of half order in time. We study inverse problems of determining the space-dependent factor in the source term from additional data at a fixed time and interior or boundary data over an appropriate time interval. We establish the global Lipschitz stability estimates in the inverse source problems. Our methods are based on Carleman estimates. Here we prove and use the Carleman estimates for a fractional diffusion equation of half order in time.

Stability in 𝐿𝑞-norm for inverse source parabolic problems

2020 ◽  
Vol 28 (6) ◽  
pp. 797-814
Author(s):  
Elena-Alexandra Melnig
Keyword(s):  
Parabolic Equations ◽  
Main Tool ◽  
Parabolic Systems ◽  
Carleman Estimates ◽  
Parabolic Problems ◽  
Lebesgue Spaces ◽  
First Order ◽  
Lipschitz Estimates ◽  
Systems Of Parabolic Equations

AbstractWe consider systems of parabolic equations coupled in zero and first order terms. We establish Lipschitz estimates in {L^{q}}-norms, {2\leq q\leq\infty}, for the source in terms of the solution in a subdomain. The main tool is a family of appropriate Carleman estimates with general weights, in Lebesgue spaces, for nonhomogeneous parabolic systems.

Inverse problem for a degenerate/singular parabolic system with Neumann boundary conditions

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Mohammed Alaoui ◽  
Abdelkarim Hajjaj ◽  
Lahcen Maniar ◽  
Jawad Salhi
Keyword(s):  
Boundary Conditions ◽  
Parabolic System ◽  
Source Term ◽  
Neumann Boundary ◽  
Stability Estimate ◽  
Carleman Estimates ◽  
Well Posedness ◽  
Degenerate Diffusion ◽  
Neumann Type ◽  
Lower Order Terms

AbstractIn this paper, we study an inverse source problem for a degenerate and singular parabolic system where the boundary conditions are of Neumann type. We consider a problem with degenerate diffusion coefficients and singular lower-order terms, both vanishing at an interior point of the space domain. In particular, we address the question of well-posedness of the problem, and then we prove a stability estimate of Lipschitz type in determining the source term by data of only one component. Our method is based on Carleman estimates, cut-off procedures and a reflection technique.

scholarly journals Global Carleman Estimates for Waves and Applications

2013 ◽  
Vol 38 (5) ◽  
pp. 823-859 ◽  
Author(s):  
Lucie Baudouin ◽  
Maya de Buhan ◽  
Sylvain Ervedoza
Keyword(s):  
Carleman Estimates
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