Hi, welcome to my page! I research non-smooth dynamical systems, the sweeping process in particular, and its applications to mechanics.

Interests

  • Sweeping process, variational and quasi-vatiational inequalities
  • Stability
  • Nonsmooth dynamical systems
  • Convex analysis
  • Unilateral constraints
  • Elastoplasticity
  • Continuum mechanics
  • Graph theory

Publications

Ivan Gudoshnikov. Regularity lost: The fundamental limitations and constraint qualifications in the problems of elastoplasticity. Discrete Contin. Dyn. Syst. (2026), early access.

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Ivan Gudoshnikov, Yang Jiao, Oleg Makarenkov, Duyu Chen. Sweeping process approach to stress analysis in elastoplastic lattice spring models with applications to network materials. Phys. Rev. E 112 (2025) 065501.

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Ivan Gudoshnikov. Elastoplasticity with softening as a state-dependent sweeping process: non-uniqueness of solutions and emergence of shear bands in lattices of springs. arXiv:2508.16333, submitted.

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Ivan Gudoshnikov, Michal Křížek. Stress solution of static linear elasticity with mixed boundary conditions via adjoint linear operators. J. Math. Anal. Appl. 543 (2025), no. 2, part 2, Paper No. 128986.

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Ivan Gudoshnikov, Oleg Makarenkov, Dmitry Rachinskiy. Formation of a nontrivial finite-time stable attractor in a class of polyhedral sweeping processes with periodic input. ESAIM Control Optim. Calc. Var. 29 (2023), Paper No. 84.

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Ivan Gudoshnikov, Oleg Makarenkov, Dmitry Rachinskiy. Finite-time stability of polyhedral sweeping processes with application to elastoplastic systems. SIAM J. Control Optim. 60 (2022), 3, 1320–1346.

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Ivan Gudoshnikov, Oleg Makarenkov. Stabilization of the response of cyclically loaded lattice spring models with plasticity. ESAIM Control Optim. Calc. Var. 27 (2021), Paper No. S8.

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Ivan Gudoshnikov, Mikhail Kamenskii, Oleg Makarenkov, Natalia Voskovskaia. One-period stability analysis of polygonal sweeping processes with application to an elastoplastic model. Math. Model. Nat. Phenom. 15 (2020), Paper No. 25.

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Ivan Gudoshnikov, Oleg Makarenkov. Structurally stable families of periodic solutions in sweeping processes of networks of elastoplastic springs. Phys. D 406 (2020), 132443.

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Lakmi Niwanthi Wadippuli Achchige, Oleg Makarenkov, Ivan Gudoshnikov. Global asymptotic stability of nonconvex sweeping processes. Discrete Contin. Dyn. Syst. Ser. B 25 (2020), no. 3, 1129–1139.

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Mikhail Kamenskii, Ivan Gudoshnikov. On the stability of perturbed semigroups in partially ordered Banach spaces. J. Math. Sci. (N.Y.) 233 (2018), no. 6, 853–874.

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Ivan Gudoshnikov, Mikhail Kamenskii, Paolo Nistri. Exponential stability of positive semigroups in Banach spaces. J. Math. Anal. Appl. 429 (2015), no. 2, 833–848.

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