Electron. J. Diff. Equ., Vol. 2015 (2015), No. 65, pp. 1-17.

Existence and convergence theorems for evolutionary hemivariational inequalities of second order

Zijia Peng, Cuie Xiao

This article concerns with a class of evolutionary hemivariational inequalities in the framework of evolution triple. Based on the Rothe method, monotonicity-compactness technique and the properties of Clarke's generalized derivative and gradient, the existence and convergence theorems to these problems are established. The main idea in the proof is using the time difference to construct the approximate problems. The work generalizes the existence results on evolution inclusions and hemivariational inequalities of second order.

Submitted September 23, 2014. Published March 18, 2015.
Math Subject Classifications: 35K15, 35K86.
Key Words: Hemivariational inequality; nonlinear evolution inclusion; Rothe method; pseudomonotone operator; Clarke's generalized gradient.

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Zijia Peng
Guangxi Key Laboratory of Universities Optimization Control
and Engineering Calculation, and School of Sciences
Guangxi University for Nationalities
Nanning, Guangxi 530006, China
email: pengzijia@126.com
  Cuie Xiao
Department of Mathematics and Computation Sciences
Hunan City University
Yiyang, Hunan 413000, China
email: xiaocuie@163.com

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