Open Access
Issue |
Math. Model. Nat. Phenom.
Volume 18, 2023
|
|
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Article Number | 17 | |
Number of page(s) | 34 | |
Section | Mathematical methods | |
DOI | https://doi.org/10.1051/mmnp/2023016 | |
Published online | 01 August 2023 |
- S. Agmon, A. Douglis and L. Nirenberg, Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions. Commun. Pure Appl. Math. 12 (1959) 623–727; II, Commun. Pure Appl. Math. 17 (1964) 35-92. [CrossRef] [Google Scholar]
- G. Allaire, Homogenization of the Navier-Stokes equations in open sets perforated with tiny holes. I. Abstract framework, volume distribution of holes. Arch. Ration. Mech. Anal. 113 (1991) 209–259. [CrossRef] [Google Scholar]
- H. Amar and D. Givoli, Mixed-dimensional modeling of time-dependent wave problems using the Panasenko construction. J. Theor. Comput. Acoust. 26 (2018) 1850034. [CrossRef] [MathSciNet] [Google Scholar]
- V.L. Berdichevsky, On averaging of periodic structures. Pr. Mat. Mech. 41 (1977) 993–1006. [Google Scholar]
- R. Bunoiu, A. Gaudiello and A. Leopardi, Asymptotic analysis of a Bingham fluid in a thin T-like shaped structure. J. Math Pures Appl. 123 (2019) 148–166. [CrossRef] [MathSciNet] [Google Scholar]
- R. Bunoiu and A. Gaudiello, On the Bingham flow in a thin Y-like shaped structure. J. Math. Fluid Mech. 24 (2022). [CrossRef] [PubMed] [Google Scholar]
- G. Cardone, G. Panasenko and I. Sirakov, Asymptotic analysis and numerical modelling of mass transport in tubular structure. Math. Models Methods Appl. Sci. 20 (2010) 397–421. [CrossRef] [MathSciNet] [Google Scholar]
- C. Conca, F. Murat and O. Pironneau, The Stokes and Navier-Stokes equations with boundary conditions involving pressure. Jap. J. Math. 20 (1994). [Google Scholar]
- A.-C. Egloffe, Study of some inverse problems for the Stokes system. Application to the lungs, These de doctorat, l’Universite Pierre et Marie Curie-Paris VI, 2012. [Google Scholar]
- H.I. Ene and E. Sanchez-Palencia, Equations de phenomenes de surface pour l’ecoulement dans un modele de milieu poreux. J. Mécan. 14 (1975) 73–108. [Google Scholar]
- L. Formaggia, D. Lamponi and A. Quarteroni, One dimensional models for blood flow in arteries, J. Eng. Math. 47 (2003) 251–276. [CrossRef] [Google Scholar]
- P. Galdi, An Introduction to the Mathematical Theory of the Navier-Stokes Equations. Steady-state Problems. Springer (2011). [Google Scholar]
- P. Galdi, R. Rannacher, A.M. Robertson and S. Turek, Hemodynamical Flows, Modeling, Analysis and Simulation. Oberwolfach Seminars, Vol. 37. Birkhäuser, Basel, Boston, Berlin (2008). [Google Scholar]
- F. Golfier, D. Lasseur and M. Quintard, Etude du probléme de Darcy-Brinkman dans une structure fluide/poreux, 14 Congres Francais de Mécanique, 1999. [Google Scholar]
- F. Harary, Graph Theory. Addison-Wesley, Reading, Massachusetts (1971). [Google Scholar]
- J.G. Heywood, R. Rannacher and S. Turek, Artificial boundaries and flux and pressure conditions for the incompressible Navier-Stokes equations. Int. J. Numer. Methods Fluids. 22 (1996) 325–352. [CrossRef] [Google Scholar]
- M.V. Korobkov, K. Pileckas and R. Russo, Solvability in a finite pipe of steady-state Navier-Stokes equations with boundary conditions involving Bernoulli pressure. Calc. Var. 59 (2020). [CrossRef] [Google Scholar]
- V. Kozlov, V. Maz’ya and A. Movchan, Asymptotic Analysis of Fields in Multi-structures. Oxford Mathematical Monographs. Oxford Science Publications. The Clarendon Press, Oxford University Press, New York (1999). [Google Scholar]
- V.A. Kozlov and S.A. Nazarov, One-dimensional model for flows in the junction of thin channels, in particular, arterial trees, Math. Sb. 208 (2017) 56–105. [CrossRef] [Google Scholar]
- O.A. Ladyzhenskaya, The Mathematical Theory of Viscous Incompressible Fluid. Gordon and Breach (1969). [Google Scholar]
- O.A. Ladyzhenskaya and V.A. Solonnikov, On some problems of vector analysis and generalized formulations of boundary value problems for the Navier-Stokes equations. Zapiski Nauchn. Sem. LOMI 59 (1976) 81–116 (in Russian); English translation in J. Sov. Math. 10 (1978) 257-286. [Google Scholar]
- Th. Levy and E. Sanchez-Palencia, On boundary conditions of flow in porous media. Int. J. Eng. Sci. 13 (1975) 923–940. [CrossRef] [Google Scholar]
- Th. Levy and E. Sanchez-Palencia, Equations and interface conditions for acoustic phenomena in porous media. J. Math. Anal. Appl. 61 (1977) 813–834. [CrossRef] [MathSciNet] [Google Scholar]
- E. Marušić-Paloka, Steady flow of a non-Newtonian fluid in unbounded channels and pipes. Math. Models Methods Appl. Sci. 10 (2000) 1425–1445. [CrossRef] [MathSciNet] [Google Scholar]
- E. Marušić-Paloka and I. Pažanin, A note on Kirchhoff junction rule for power-law fluids. Z. Naturf. A 70 (2015) 695–702. [CrossRef] [Google Scholar]
- V.G. Maz’ya and A. Slutskii, Asymptotic analysis of the Navier-Stokes system in a plane domain with thin channels. Asymptotic Anal. 23 (2000) 59–89. [MathSciNet] [Google Scholar]
- G. Panasenko, Method of asymptotic partial decomposition of Domain. Math. Models Methods Appl. Sci. 8 (1998) 139–156. [CrossRef] [Google Scholar]
- G. Panasenko, Asymptotic expansion of the solution of Navier-Stokes equation in a tube structure. C.R. Acad. Sci. Paris Serie Ilb 326 (1998) 867–872. [CrossRef] [Google Scholar]
- G. Panasenko, Partial asymptotic decomposition of domain: Navier-Stokes equation in tube structure. C.R. Acad. Sci. Paris Seerie IIb 326 (1998) 893–898. [Google Scholar]
- G. Panasenko, Multi-scale Modeling for Structures and Composites. Springer, Dordrecht (2005). [Google Scholar]
- G. Panasenko and K. Pileckas, Divergence equation in thin-tube Structure. Appl. Anal. 94 (2015) 1450–1459. [CrossRef] [MathSciNet] [Google Scholar]
- G. Panasenko and K. Pileckas, Flows in a tube structure: equation on the graph. J. Math. Phys. 55 (2014) 081505 [CrossRef] [MathSciNet] [Google Scholar]
- G. Panasenko and K. Pileckas, Asymptotic analysis of the non-steady Navier-Stokes equations in a tube structure. I. The case without boundary layer-in-time. Nonlinear Anal. Ser. A Theory Methods Applic. 122 (2015) 125–168. [CrossRef] [Google Scholar]
- G. Panasenko, K. Pileckas and B. Vernescu, Steady state non-Newtonian flow with strain rate dependent viscosity in thin tube structure with no-slop boundary condition. Math. Model. Natural Phenomena 17 (2022) Art. No. 18. [Google Scholar]
- O. Pironneau, Conditions aux limites sur la pression pour les equations de Stokes et de Navier-Stokes. C.R. Acad. Sci. Paris Ser. I Math. 303 (1986) 403–406. [Google Scholar]
- A. Quarteroni and L. Formaggia, Mathematical modelling and numerical simulation of the cardiovascular system, in Modelling of Living Systems, Handbook of Numerical Analysis Series, edited by N. Ayache (2002). [Google Scholar]
- A. Quarteroni and A. Veneziani, Analysis of a geometrical multiscale model based on the coupling of ODEs and PDEs for blood flow simulations. Multiscale Model. Simul. 1 (2003) 173–195. [CrossRef] [MathSciNet] [Google Scholar]
- E. Sanchez-Palencia, Equations aux derivees partielles. Solutions periodiques par rapport aux variables d’espace et applications. Compt. Rend. Acad. Sci. Paris, seer. A (1970) 1129–1132. [Google Scholar]
- E. Sanchez-Palencia, Non-homogeneous Media and Vibration Theory. Springer-Verlag, New York (1980). [Google Scholar]
- L. Tartar, Homogenization. Cours Peccot. College de France, Paris (1977). [Google Scholar]
- L. Tartar, Topics in Non Linear Analysis. Report of the University of Orsay, France (1978). [Google Scholar]
- R. Temam, Navier-Stokes Equations. North-Holland Pub. Company (1977). [Google Scholar]
- D.B. Volkov, On averaging of some boundary value problems in domains with periodic structure. USSR Comp. Math. and Math. Phys. 22 (1982) 117–128. [CrossRef] [Google Scholar]
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