Chen, PanyuMateos González, ÁlvaroMertz, Laurent2025-04-082025-04-082025-02Chen, P., Mateos González, Á., & Mertz, L. (2025). An elementary approach based on variational inequalities for modeling a friction-based locomotion problem. Applied Mathematics Letters, 160. https://doi.org/10.1016/J.AML.2024.1093050893-965910.1016/j.aml.2024.109305https://hdl.handle.net/20.500.14352/119345L.M. is thankful for support through NSFC Grant No. 12271364 and GRF Grant No. 11302823. We thank the anonymous referee for important feedback.We propose an elementary proof based on a penalization technique to show the existence and uniqueness of the solution to a system of variational inequalities modeling the friction-based motion of a two-body crawling system. Here for each body, the static and dynamic friction coefficients are equal.engjournal article1873-5452https://doi.org/10.1016/j.aml.2024.109305https://www.sciencedirect.com/science/article/pii/S0893965924003252?via%3Dihubrestricted access517.9751:57539.62Variational inequalitiesMoreau–Yosida regularizationBiolocomotionDry frictionMatemáticas (Matemáticas)Funciones (Matemáticas)Biomatemáticas12 Matemáticas1202.04 Cálculo de Variaciones2404 Biomatemáticas2205.05 Fricción