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Applicable Analysis
An International Journal
Volume 98, 2019 - Issue 10
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Articles

Ritz–Galerkin method for solving an inverse problem of parabolic equation with moving boundaries and integral condition

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Pages 1741-1755 | Received 23 Jan 2018, Accepted 25 Jan 2018, Published online: 11 Feb 2018
 

ABSTRACT

In this paper, we consider an inverse problem for parabolic equation with moving boundaries and integral condition. Existence and uniqueness are proved using tool from double-layer heat potential and Volterra integral equations of the second kind. For computation part, the Ritz–Galerkin method is first implemented to get an approximate solution of intermediate function H(x, t), and then based on relationships between H(x, t) and λ(t),u(x,t), respectively, numerical solutions of λ(t) and u(x, t) are obtained. Finally, numerical examples are presented to show the validity and applicability of our method.

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Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

The present investigation was supported in part by the National Natural Science Foundation of the People’s Republic of China [grant number 11201070]; the Science Research Fund of Department of Guangdong Province of the People’s Republic of China [grant number Yq2013161].

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