An inverse heat equation in two space dimensions

B. Emamizadeh

doi:10.1016/j.aml.2003.09.009

An inverse heat equation in two space dimensions

B. Emamizadeh

Research output: Journal Publication › Article › peer-review

1 Citation (Scopus)

Abstract

The uniqueness for an inverse heat equation in two space dimensions was proved. It was observed that the result presented to two space dimensions were extended. It was also confirmed that that the same ideas could be used in order to generalize the results presented to any space dimensions. By using Lemma3, the function w was found to be a distributional solution of (1.1) in D× (-T,T). The Lemma 2 could be applied to conclude that u=0 in D₂(0,T).

Original language	English
Pages (from-to)	1161-1165
Number of pages	5
Journal	Applied Mathematics Letters
Volume	17
Issue number	10
DOIs	https://doi.org/10.1016/j.aml.2003.09.009
Publication status	Published - 2004
Externally published	Yes

Keywords

Heat equation
Inverse problem
Unique continuation
Uniqueness

ASJC Scopus subject areas

Applied Mathematics

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10.1016/j.aml.2003.09.009

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title = "An inverse heat equation in two space dimensions",

abstract = "The uniqueness for an inverse heat equation in two space dimensions was proved. It was observed that the result presented to two space dimensions were extended. It was also confirmed that that the same ideas could be used in order to generalize the results presented to any space dimensions. By using Lemma3, the function w was found to be a distributional solution of (1.1) in D× (-T,T). The Lemma 2 could be applied to conclude that u=0 in D2(0,T).",

keywords = "Heat equation, Inverse problem, Unique continuation, Uniqueness",

author = "B. Emamizadeh",

note = "Funding Information: The author thanks Professor A.G. Ramm for making valuable comments on the primary version of the paper. He also thanks Dr. H. Azary for fruitful discussions concerning this problem. He is also grateful to Institute for Studies in Theoretical Physics and Mathematics for partial financial support.",

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AU - Emamizadeh, B.

N1 - Funding Information: The author thanks Professor A.G. Ramm for making valuable comments on the primary version of the paper. He also thanks Dr. H. Azary for fruitful discussions concerning this problem. He is also grateful to Institute for Studies in Theoretical Physics and Mathematics for partial financial support.

PY - 2004

Y1 - 2004

N2 - The uniqueness for an inverse heat equation in two space dimensions was proved. It was observed that the result presented to two space dimensions were extended. It was also confirmed that that the same ideas could be used in order to generalize the results presented to any space dimensions. By using Lemma3, the function w was found to be a distributional solution of (1.1) in D× (-T,T). The Lemma 2 could be applied to conclude that u=0 in D2(0,T).

AB - The uniqueness for an inverse heat equation in two space dimensions was proved. It was observed that the result presented to two space dimensions were extended. It was also confirmed that that the same ideas could be used in order to generalize the results presented to any space dimensions. By using Lemma3, the function w was found to be a distributional solution of (1.1) in D× (-T,T). The Lemma 2 could be applied to conclude that u=0 in D2(0,T).

KW - Heat equation

KW - Inverse problem

KW - Unique continuation

KW - Uniqueness

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SP - 1161

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JO - Applied Mathematics Letters

JF - Applied Mathematics Letters

IS - 10

ER -

An inverse heat equation in two space dimensions

Abstract

Keywords

ASJC Scopus subject areas

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