Convergence analysis on Browder-Tikhonov regularization for second-order evolution hemivariational inequality

doi:10.1007/s10483-015-1989-9

Applied Mathematics and Mechanics (English Edition) ›› 2015, Vol. 36 ›› Issue (10): 1371-1382.doi: https://doi.org/10.1007/s10483-015-1989-9

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Convergence analysis on Browder-Tikhonov regularization for second-order evolution hemivariational inequality

Yibin XIAO¹, Guoji TANG², Xianjun LONG³, Nanjing HUANG⁴

1. School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu 611731, China;
2. School of Science, Guangxi University for Nationalities, Nanning 530006, China;
3. College of Mathematics and Statistics, Chongqing Technology and Business University, Chongqing 400067, China;
4. Department of Mathematics, Sichuan University, Chengdu 610064, China

Received:2014-12-28 Revised:2015-03-13 Online:2015-10-01 Published:2015-10-01
Contact: Yibin XIAO E-mail:xiaoyb9999@hotmail.com
Supported by:
Project supported by the National Natural Science Foundation of China (Nos. 11101069, 11171237, 11471059, and 81171411), the China Postdoctoral Science Foundation (Nos. 2014M552328 and 2015T80967), and the Scientific Research Foundation for the Returned Overseas Chinese Scholars, State Education Ministry

Abstract

Abstract: This paper studies the Browder-Tikhonov regularization of a second-order evolution hemivariational inequality (SOEHVI) with non-coercive operators. With duality mapping, the regularized formulations and a derived first-order evolution hemivariational inequality (FOEHVI) for the problem considered are presented. By applying the Browder-Tikhonov regularization method to the derived FOEHVI, a sequence of regularized solutions to the regularized SOEHVI is constructed, and the strong convergence of the whole sequence of regularized solutions to a solution to the problem is proved.

Key words: Clarke's generalized gradient, Browder-Tikhonov regularization, second-order evolution hemivariational inequality (SOEHVI)

2010 MSC Number:

O224
O177

Yibin XIAO, Guoji TANG, Xianjun LONG, Nanjing HUANG. Convergence analysis on Browder-Tikhonov regularization for second-order evolution hemivariational inequality. Applied Mathematics and Mechanics (English Edition), 2015, 36(10): 1371-1382.

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References

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Convergence analysis on Browder-Tikhonov regularization for second-order evolution hemivariational inequality

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