A Note on an Inverse Problem Related to the 3-D Heat Equation

Cannon, John R.; Esteva, Salvador Pérez

doi:10.1007/978-3-0348-7014-6_10

Cited by 5 publications

(2 citation statements)

References 4 publications

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“…Canon and Esteva [7] proved a logarithmic stability estimate for the determination of the support of a source term in a one dimension parabolic equation from a boundary measurement. This result was extended to three dimension heat equation in [8]. The case of a non local measurement was considered by Canon and Lin in [9,10].…”

Section: 3)mentioning

confidence: 85%

Logarithmic stability in determining the time-dependent zero order coefficient in a parabolic equation from a partial Dirichlet-to-Neumann map. Application to the determination of a nonlinear term

Choulli

Kian

2018

Journal de Mathématiques Pures et Appliquées

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Abstract. We give a new stability estimate for the problem of determining the time-dependent zero order coefficient in a parabolic equation from a partial parabolic Dirichlet-to-Neumann map. The novelty of our result is that, contrary to the previous works, we do not need any measurement on the final time. We also show how this result can be used to establish a stability estimate for the problem of determining the nonlinear term in a semilinear parabolic equation from the corresponding "linearized" Dirichlet-to-Neumann map. The key ingredient in our analysis is a parabolic version of an elliptic Carleman inequality due to Bukhgeim and Uhlmann [6]. This parabolic Carleman inequality enters in an essential way in the construction of CGO solutions that vanish at a part of the lateral boundary.

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