What does this research mean for the field?

A dynamic bilateral contact model for viscoelastic materials with Tresca's friction law and infinite memory exhibits global well-posedness and exponential stability. Novelty: ClaimNovelty.INCREMENTAL. Consensus alignment: ConsensusAlignment.NEUTRAL.

What question did this study set out to answer?

To establish the mathematical well-posedness and asymptotic decay rate for dynamic viscoelastic materials undergoing bilateral contact with Tresca friction and infinite memory.

September 14, 2026Mathematics and Mechanics of SolidsOpen Access

Semigroup well-posedness and exponential decay of a viscoelastic bilateral contact model with Tresca’s law and infinite memory

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Authors

HKHoud KhireddineUniversité de M'Sila BBBenyattou BenabderrahmaneHigher National Veterinary School ALAbdelaziz LimamUniversité des Sciences et de la Technologie d'Oran Mohamed Boudiaf

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Implication

Theoretical analysis demonstrates global well-posedness and exponential decay in viscoelastic bilateral contact systems with dry friction, highlighting long-term system stability.

Key Points

To establish the mathematical well-posedness and asymptotic decay rate for dynamic viscoelastic materials undergoing bilateral contact with Tresca friction and infinite memory.
Formulated a dynamic bilateral contact problem incorporating Tresca's friction law and a nonlinear constitutive relation with memory history.
Applied operator semigroup theory to demonstrate the existence and uniqueness of global solutions.
Employed an energy multiplier method under suitable structural assumptions to analyze the asymptotic stabilization of the system.
Proved the global well-posedness of the nonlinear viscoelastic contact model within the semigroup framework.
Demonstrated exponential energy decay and long-term stability of the contact system under specified growth and memory kernel conditions.

Cite This Study

Khireddine et al. (2026) studied this question.

synapsesocial.com/papers/6aa7b3aa0926e14a848b2d22 https://doi.org/10.1177/10812865261484142

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Implication

Theoretical analysis demonstrates global well-posedness and exponential decay in viscoelastic bilateral contact systems with dry friction, highlighting long-term system stability.

Semigroup well-posedness and exponential decay of a viscoelastic bilateral contact model with Tresca’s law and infinite memory

Discussion

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Implication

Key Points

Cite This Study

Semigroup well-posedness and exponential decay of a viscoelastic bilateral contact model with Tresca’s law and infinite memory

Discussion

Member takes

Implication

Key Points

Cite This Study

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