In this paper we deal with a second order evolution inclusion involving a multivalued term generated by a Clarke subdifferential of a locally Lipschitz potential. For this problem we construct a double step time-semidiscrete approximation, known as the Rothe scheme. We study a sequence of solutions of the semidiscrete approximate problems and provide its weak convergence to a limit element that is a solution of the original problem.

翻译：本文研究一类涉及由局部Lipschitz位势的Clarke次微分生成的多值项的二阶发展包含问题。针对该问题，我们构造了双步时间半离散逼近格式（即Rothe格式）。通过研究半离散逼近问题解序列的性质，证明了该序列弱收敛于原始问题的解。