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Convergence of Rothe scheme for a class of dynamic variational inequalities involving Clarke subdifferential
- Source :
- Applicable Analysis. 97:2189-2209
- Publication Year :
- 2017
- Publisher :
- Informa UK Limited, 2017.
-
Abstract
- In the first part of the paper we deal with a second-order evolution variational inequality involving a multivalued term generated by a Clarke subdifferential of a locally Lipschitz potential. For this problem we construct a 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. Next, we show that the solution is unique and the convergence is strong. In the second part of the paper, we consider a dynamic visco-elastic problem of contact mechanics. We assume that the contact process is governed by a normal damped response condition with a unilateral constraint and the body is non-clamped. The mechanical problem in its weak formulation reduces to a variational–hemivariational inequality that can be solved by finding a solution of a corresponding abstract problem related to one studied in the first part of the paper. Hence, we a...
- Subjects :
- Sequence
Weak convergence
Applied Mathematics
010102 general mathematics
Mathematical analysis
Subderivative
Weak formulation
Lipschitz continuity
01 natural sciences
010101 applied mathematics
Variational inequality
Convergence (routing)
Limit (mathematics)
0101 mathematics
Analysis
Mathematics
Subjects
Details
- ISSN :
- 1563504X and 00036811
- Volume :
- 97
- Database :
- OpenAIRE
- Journal :
- Applicable Analysis
- Accession number :
- edsair.doi.dedup.....8577ea31100105094edca9a5efb58477