The problems of the project are presented in local press:
Scientific papers:
1. G. Panasenko, K. Pileckas, B. Vernescu. Steady state non-Newtonian flow in thin tube structure: equation on the graph. Algebra i Analiz, 33:2, 197–214 , 2021.
2. R. Juodagalvytė, G. Panasenko, K. Pileckas. Steady-State Navier-Stokes Equations in Thin Tube Structure with the Bernoulli Pressure Inflow Boundary Conditions: Asymptotic Analysis, Mathematics 2021, 9(19). https://doi.org/10.3390/math9192433
3. C. Bertoglio, D. Nolte, G. Panasenko, K. Pileckas. Reconstruction of the Pressure in the Method of Asymptotic Partial Decomposition for the Flows in Tube Structures. SIAM J. Appl. Math., 81(5), 2083–2110, 2021. https://doi.org/10.1137/20M1388462
4. G. Panasenko, K. Pileckas, B. Vernescu. Steady state non-Newtonian flow with strain rate dependent viscosity in thin tube structure with no slip boundary condition, Mathematical Models of Natural Phenomena, Vol. 17, 2022, 36 pages. https://doi.org/10.1051/mmnp/2022005
5. V. Šumskas, R. Čiegis. Finite volume ADI scheme for hybrid dimension heat conduction problems set in a cross-shaped domain, Lithuanian Mathematical Journal, Vol. 62, No. 2, 2022, pp. 239–258. https://doi.org/10.1007/s10986-022-09561-0
6. É. Canon, F. Chardard, G. Panasenko, O. Štikonienė. Asymptotics and discretization of a weakly singular kernel: Application to viscous flows in a network of thin tubes, Journal of Computational Physics, Vol. 491, 2023, 35 pages. https://doi.org/10.1016/j.jcp.2023.112327
7. G. Panasenko, K. Pileckas. Non-stationary Poiseuille flow of a non-Newtonian fluid with the shear rate dependent viscosity, Advances in Nonlinear Analysis, vol. 12, no. 1, 2023, pp. 20220259. https://doi.org/10.1515/anona-2022-0259
8. G. Panasenko, K. Pileckas. Partial asymptotic dimension reduction for steady state non-Newtonian flow with strain rate dependent viscosity in thin tube structure. Journal of Mathematical Fluid Mechanics, vol. 25, No.11, 2023. https://doi.org/10.1007/s00021-022-00749-5
9. K. Kaulakytė, N. Kozulinas, G. Panasenko, K. Pileckas, V. Šumskas. Poiseuille-Type Approximations for Axisymmetric Flow in a Thin Tube with Thin Stiff Elastic Wall. Mathematics 2023, 11(9), 2106. https://doi.org/10.3390/math11092106
10. G. Panasenko, K. Pileckas. Pressure boundary conditions for viscous flows in thin tube structures: Stokes equations with locally distributed Brinkman term, Mathematical Models of Natural Phenomena, 2023. https://doi.org/10.1051/mmnp/2023016
11. G. Panasenko, N. Kozulinas, K. Pileckas, V. Šumskas. Numerical study of the equation on the graph for the steady state non-Newtonian flow in thin tube structure. Accepted to Journal Mathematical Modelling and Analysis, 2023.
12. G. Panasenko, R. Stavre. Asymptotic Solution for a Visco-Elastic Thin Plate; Quasistatic and Dynamic Cases. Mathematics, 2023, 11(13), 2847. https://doi.org/10.3390/math11132847
13. A. Belyaev, A. Bouchnita, N. Kozulinas, G. Panassenko, V. Volpert. Multiphase continuum modeling to identify the key factors contributing to thrombosis in the left atrium appendage. Submitted.
