This work establishes existence and uniqueness of solutions for hysteresis models in heterogeneous media, suggesting practical implications for computational methods.
In this work, we propose a multiscale finite element method for solving heterogeneous nonlinear parabolic problems involving Duhem operators that model hysteresis in spatially varying media. A formulation of the method is introduced to facilitate the mathematical analysis, linking microscopic heterogeneities to macroscopic behavior. We establish the existence, uniqueness and boundedness of the numerical solution for both periodic and Dirichlet coupling scenarios, laying a strong foundation for the practical implementation of the multiscale method in computational settings.
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Kakeu et al. (2026) studied this question.
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