State-Dependent Implicit Sweeping Process in the Framework of Quasistatic Evolution Quasi-Variational Inequalities
Abstract This paper deals with the existence and uniqueness of solutions for a class of state-dependent sweeping processes with constrained velocity in Hilbert spaces without using any compactness assumption, which is known to be an open problem. To overcome the difficulty, we introduce a new notion...
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| Autor*in: |
Adly, Samir [verfasserIn] |
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| Format: |
Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2018 |
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| Systematik: |
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| Anmerkung: |
© Springer Science+Business Media, LLC, part of Springer Nature 2018 |
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| Übergeordnetes Werk: |
Enthalten in: Journal of optimization theory and applications - Springer US, 1967, 182(2018), 2 vom: 01. Nov., Seite 473-493 |
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| Übergeordnetes Werk: |
volume:182 ; year:2018 ; number:2 ; day:01 ; month:11 ; pages:473-493 |
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| DOI / URN: |
10.1007/s10957-018-1427-x |
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| 520 | |a Abstract This paper deals with the existence and uniqueness of solutions for a class of state-dependent sweeping processes with constrained velocity in Hilbert spaces without using any compactness assumption, which is known to be an open problem. To overcome the difficulty, we introduce a new notion called hypomonotonicity-like of the normal cone to the moving set, which is satisfied by many important cases. Combining this latter notion with an adapted Moreau’s catching-up algorithm and a Cauchy technique, we obtain the strong convergence of approximate solutions to the unique solution, which is a fundamental property. Using standard tools from convex analysis, we show the equivalence between this implicit state-dependent sweeping processes and quasistatic evolution quasi-variational inequalities. As an application, we study the state-dependent quasistatic frictional contact problem involving viscoelastic materials with short memory in contact mechanics. | ||
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state-dependent implicit sweeping process in the framework of quasistatic evolution quasi-variational inequalities |
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State-Dependent Implicit Sweeping Process in the Framework of Quasistatic Evolution Quasi-Variational Inequalities |
| abstract |
Abstract This paper deals with the existence and uniqueness of solutions for a class of state-dependent sweeping processes with constrained velocity in Hilbert spaces without using any compactness assumption, which is known to be an open problem. To overcome the difficulty, we introduce a new notion called hypomonotonicity-like of the normal cone to the moving set, which is satisfied by many important cases. Combining this latter notion with an adapted Moreau’s catching-up algorithm and a Cauchy technique, we obtain the strong convergence of approximate solutions to the unique solution, which is a fundamental property. Using standard tools from convex analysis, we show the equivalence between this implicit state-dependent sweeping processes and quasistatic evolution quasi-variational inequalities. As an application, we study the state-dependent quasistatic frictional contact problem involving viscoelastic materials with short memory in contact mechanics. © Springer Science+Business Media, LLC, part of Springer Nature 2018 |
| abstractGer |
Abstract This paper deals with the existence and uniqueness of solutions for a class of state-dependent sweeping processes with constrained velocity in Hilbert spaces without using any compactness assumption, which is known to be an open problem. To overcome the difficulty, we introduce a new notion called hypomonotonicity-like of the normal cone to the moving set, which is satisfied by many important cases. Combining this latter notion with an adapted Moreau’s catching-up algorithm and a Cauchy technique, we obtain the strong convergence of approximate solutions to the unique solution, which is a fundamental property. Using standard tools from convex analysis, we show the equivalence between this implicit state-dependent sweeping processes and quasistatic evolution quasi-variational inequalities. As an application, we study the state-dependent quasistatic frictional contact problem involving viscoelastic materials with short memory in contact mechanics. © Springer Science+Business Media, LLC, part of Springer Nature 2018 |
| abstract_unstemmed |
Abstract This paper deals with the existence and uniqueness of solutions for a class of state-dependent sweeping processes with constrained velocity in Hilbert spaces without using any compactness assumption, which is known to be an open problem. To overcome the difficulty, we introduce a new notion called hypomonotonicity-like of the normal cone to the moving set, which is satisfied by many important cases. Combining this latter notion with an adapted Moreau’s catching-up algorithm and a Cauchy technique, we obtain the strong convergence of approximate solutions to the unique solution, which is a fundamental property. Using standard tools from convex analysis, we show the equivalence between this implicit state-dependent sweeping processes and quasistatic evolution quasi-variational inequalities. As an application, we study the state-dependent quasistatic frictional contact problem involving viscoelastic materials with short memory in contact mechanics. © Springer Science+Business Media, LLC, part of Springer Nature 2018 |
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State-Dependent Implicit Sweeping Process in the Framework of Quasistatic Evolution Quasi-Variational Inequalities |
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Haddad, Tahar Le, Ba Khiet |
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