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Article

A Well-Posed Evolutionary Inclusion in Mechanics

Laboratoire de Modélisation Pluridisciplinaire et Simulations, University of Perpignan Via Domitia, 52 Avenue Paul Alduy, 66860 Perpignan, France
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Author to whom correspondence should be addressed.
These authors contributed equally to this work.
Axioms 2025, 14(6), 448; https://doi.org/10.3390/axioms14060448
Submission received: 5 May 2025 / Revised: 29 May 2025 / Accepted: 5 June 2025 / Published: 6 June 2025
(This article belongs to the Special Issue Recent Trends in Numerical Methods for Functional Equations)

Abstract

We consider an evolutionary inclusion associated with a time-dependent convex in an abstract Hilbert space. We recall a unique solvability result obtained based on arguments of nonlinear equations with maximal monotone operators combined with a penalty method. Then, we state and prove two well-posedness results. Next, we provide three examples of such inclusions that arise in mechanics. The first one concerns an elastic–perfectly plastic constitutive law, while the last two examples are mathematical models that describe the equilibrium of an elastic body and an elastic–perfectly plastic body, respectively, in frictional contact with an obstacle. The contact is bilateral and the friction is modeled with the Tresca friction law. We use our abstract results in the study of these examples to provide the convergence of the solution with respect to the data.
Keywords: evolutionary inclusion; time-dependent convex; well-posedness results; elastic material; plastic material; frictional contact; uniform convergence evolutionary inclusion; time-dependent convex; well-posedness results; elastic material; plastic material; frictional contact; uniform convergence

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MDPI and ACS Style

Mansour, R.; Sofonea, M. A Well-Posed Evolutionary Inclusion in Mechanics. Axioms 2025, 14, 448. https://doi.org/10.3390/axioms14060448

AMA Style

Mansour R, Sofonea M. A Well-Posed Evolutionary Inclusion in Mechanics. Axioms. 2025; 14(6):448. https://doi.org/10.3390/axioms14060448

Chicago/Turabian Style

Mansour, Rawane, and Mircea Sofonea. 2025. "A Well-Posed Evolutionary Inclusion in Mechanics" Axioms 14, no. 6: 448. https://doi.org/10.3390/axioms14060448

APA Style

Mansour, R., & Sofonea, M. (2025). A Well-Posed Evolutionary Inclusion in Mechanics. Axioms, 14(6), 448. https://doi.org/10.3390/axioms14060448

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