Reconstruction of two time independent coefficients in an inverse problem for a phase field system

N. Baranibalan; K. Sakthivel; K. Balachandran; J. H. Kim

doi:10.1016/j.na.2009.11.027

Reconstruction of two time independent coefficients in an inverse problem for a phase field system

N. Baranibalan, K. Sakthivel, K. Balachandran, J. H. Kim

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

5 Citations (Scopus)

Abstract

In this paper we present stability results concerning the inverse problem of determining two time independent coefficients for a phase field system in a bounded domain Ω ⊂ Rⁿ for the dimension n ≤ 3 with a single observation on a subdomain ω {double subset} Ω and the Sobolev norm of certain partial derivatives of the solutions at a fixed positive time θ ∈ (0, T) over the whole spatial domain. The proof of these results relies on an appropriate Carleman estimate for the phase field system.

Original language	English
Pages (from-to)	2841-2851
Number of pages	11
Journal	Nonlinear Analysis, Theory, Methods and Applications
Volume	72
Issue number	6
DOIs	https://doi.org/10.1016/j.na.2009.11.027
Publication status	Published - 2009 May 15

Bibliographical note

Funding Information:
The work of the second author was supported by the Brain Korea 21 project at Yonsei University, 2008. The work of the fourth author was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (2009-8-0796) and also in part by the MKE and KIAT through the Workforce Development Program in Strategic Technology.

All Science Journal Classification (ASJC) codes

Analysis
Applied Mathematics

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10.1016/j.na.2009.11.027

Cite this

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title = "Reconstruction of two time independent coefficients in an inverse problem for a phase field system",

abstract = "In this paper we present stability results concerning the inverse problem of determining two time independent coefficients for a phase field system in a bounded domain Ω ⊂ Rn for the dimension n ≤ 3 with a single observation on a subdomain ω {double subset} Ω and the Sobolev norm of certain partial derivatives of the solutions at a fixed positive time θ ∈ (0, T) over the whole spatial domain. The proof of these results relies on an appropriate Carleman estimate for the phase field system.",

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AU - Baranibalan, N.

AU - Sakthivel, K.

AU - Balachandran, K.

AU - Kim, J. H.

N1 - Funding Information: The work of the second author was supported by the Brain Korea 21 project at Yonsei University, 2008. The work of the fourth author was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (2009-8-0796) and also in part by the MKE and KIAT through the Workforce Development Program in Strategic Technology.

PY - 2009/5/15

Y1 - 2009/5/15

N2 - In this paper we present stability results concerning the inverse problem of determining two time independent coefficients for a phase field system in a bounded domain Ω ⊂ Rn for the dimension n ≤ 3 with a single observation on a subdomain ω {double subset} Ω and the Sobolev norm of certain partial derivatives of the solutions at a fixed positive time θ ∈ (0, T) over the whole spatial domain. The proof of these results relies on an appropriate Carleman estimate for the phase field system.

AB - In this paper we present stability results concerning the inverse problem of determining two time independent coefficients for a phase field system in a bounded domain Ω ⊂ Rn for the dimension n ≤ 3 with a single observation on a subdomain ω {double subset} Ω and the Sobolev norm of certain partial derivatives of the solutions at a fixed positive time θ ∈ (0, T) over the whole spatial domain. The proof of these results relies on an appropriate Carleman estimate for the phase field system.

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Reconstruction of two time independent coefficients in an inverse problem for a phase field system

Abstract

Bibliographical note

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