Mathematical Methods in the Applied Sciences

Volume 42, Issue 18 pp. 6284-6300

RESEARCH ARTICLE

The global solvability and asymptotic behavior of a transmission problem for Kirchhoff-type wave equations with memory source on the boundary

Zhiqing Liu,

Zhiqing Liu

School of Mathematical Sciences, Ocean University of China, Qingdao, 266100 China

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Zhong Bo Fang,

Corresponding Author

Zhong Bo Fang

[email protected]

orcid.org/0000-0001-5569-0131

School of Mathematical Sciences, Ocean University of China, Qingdao, 266100 China

Correspondence

Zhong Bo Fang, School of Mathematical Sciences, Ocean University of China, Qingdao 266100, China.

Email: [email protected]

Communicated by: N. Hyvonen

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Zhiqing Liu,

Zhiqing Liu

School of Mathematical Sciences, Ocean University of China, Qingdao, 266100 China

Search for more papers by this author

Zhong Bo Fang,

Corresponding Author

Zhong Bo Fang

[email protected]

orcid.org/0000-0001-5569-0131

School of Mathematical Sciences, Ocean University of China, Qingdao, 266100 China

Correspondence

Zhong Bo Fang, School of Mathematical Sciences, Ocean University of China, Qingdao 266100, China.

Email: [email protected]

Communicated by: N. Hyvonen

Search for more papers by this author

First published: 24 July 2019

https://doi.org/10.1002/mma.5722

Citations: 4

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Abstract

A transmission problem for Kirchhoff-type wave equations with memory source term on one part of the boundary feedback is considered. By using the Faedo-Galerkin approximation technique, the method of Lyapunov functional and the energy perturbation technique, we establish well-posedness of global solution and derive a general decay estimate of the energy.

CONFLICTS OF INTEREST

This work does not have any conflicts of interest.

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Volume42, Issue18

December 2019

Pages 6284-6300

The global solvability and asymptotic behavior of a transmission problem for Kirchhoff-type wave equations with memory source on the boundary

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The global solvability and asymptotic behavior of a transmission problem for Kirchhoff-type wave equations with memory source on the boundary

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