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Volume 8, Number 6, 2018, Pages 1664-1678                                                                DOI:10.11948/2018.1664
A Class of differential inverse variational inequalities in finite dimensional spaces
Jun Feng,Wei Li,Hui Chen,Yuanchun Chen
Keywords:Differential inverse variational inequality, Caratheodory weak solution, Euler time-stepping procedure, algorithm.
Abstract:
      In this paper, we study a class of differential inverse variational inequality (for short, DIVI) in finite dimensional Euclidean spaces. Firstly, under some suitable assumptions, we obtain linear growth of the solution set for the inverse variational inequalities. Secondly, we prove existence theorems for weak solutions of the DIVI in the weak sense of Carath\""{e}odory by using measurable selection lemma. Thirdly, by employing the results from differential inclusions we establish a convergence result on Euler time dependent procedure for solving the DIVI. Finally, we give a numerical experiment to verify the validity of the algorithm.
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