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2013 | 11 | 6 | 1112-1128
Tytuł artykułu

Global existence for a system of nonlocal PDEs with applications to chemically reacting incompressible fluids

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EN
Abstrakty
EN
We show global existence for a class of models of fluids that change their properties depending on the concentration of a chemical. We allow that the stress tensor in (t, x) depends on the velocity and concentration at other points and times. The example we have in mind foremost are materials with memory.
Twórcy
  • Department of Mathematical Analysis, Faculty of Mathematics and Physics, Charles University in Prague, Sokolovská 83, Praha 8, 18000, Czech Republic, barta@karlin.mff.cuni.cz
Bibliografia
  • [1] Adams R.A., Fournier J.J.F., Sobolev Spaces, 2nd ed., Pure Appl. Math. (Amst.), 140, Elsevier, Amsterdam, 2003
  • [2] Bulíček M., Málek J., Rajagopal K.R., Mathematical analysis of unsteady flows of fluids with pressure, shear-rate, and temperature dependent material moduli that slip at solid boundaries, SIAM J. Math. Anal., 2009, 41(2), 665–707 http://dx.doi.org/10.1137/07069540X[Crossref][WoS]
  • [3] Bulíček M., Málek J., Rajagopal K.R., Mathematical results concerning unsteady flows of chemically reacting incompressible fluids, In: Partial Differential Equations and Fluid Mechanics, London Math. Soc. Lecture Note Ser., 364, Cambridge University Press, Cambridge, 2009, 26–53 http://dx.doi.org/10.1017/CBO9781139107112.003[Crossref]
  • [4] Gajewski H., Gröger K., Zacharias K., Nichtlineare Operatorgleichungen und Operatordifferentialgleichungen, Math. Lehrbucher und Monogr., 38, Akademie, Berlin, 1974
  • [5] Gripenberg G., Londen S.-O., Staffans O., Volterra Integral and Functional Equations, Encyclopedia Math. Appl., 34, Cambridge University Press, Cambridge, 1990 http://dx.doi.org/10.1017/CBO9780511662805[Crossref]
  • [6] Málek J., Nečas J., Rokyta M., Růžička M., Weak and Measure-Valued Solutions to Evolutionary PDE, Appl. Math. Math. Comput., 13, Chapman & Hall, London, 1996
  • [7] Prüss J., Evolutionary Integral Equations and Applications, Monogr. Math., 87, Birkhäuser, Basel, 1993 http://dx.doi.org/10.1007/978-3-0348-8570-6[Crossref]
  • [8] Rajagopal K.R., Wineman A.S., Applications of viscoelastic clock models in biomechanics, Acta Mech., 2010, 213(3–4), 255–266 http://dx.doi.org/10.1007/s00707-009-0262-4[Crossref][WoS]
  • [9] Renardy M., Hrusa W.J., Nohel J.A., Mathematical Problems in Viscoelasticity, Pitman Monogr. Surveys Pure Appl. Math., 35, Longman Scientific & Technical, Harlow; John Wiley & Sons, New York, 1987
  • [10] Simon J., Compact sets in the space Lp(0; T;B), Ann. Mat. Pura Appl., 1987, 146, 65–96 http://dx.doi.org/10.1007/BF01762360
  • [11] Vorotnikov D.A., Zvyagin V.G., On the convergence of solutions of a regularized problem for the equations of motion of a Jeffery viscoelastic medium to the solutions of the original problem, J. Math. Sci. (N.Y.), 2007, 144(5), 4398–4408 http://dx.doi.org/10.1007/s10958-007-0277-0[Crossref]
  • [12] Zvyagin V.G., Dmitrienko V.T., On weak solutions of a regularized model of a viscoelastic fluid, Differ. Equ., 2002, 38(12), 1731–1744 http://dx.doi.org/10.1023/A:1023860129831[Crossref]
Typ dokumentu
Bibliografia
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bwmeta1.element.doi-10_2478_s11533-013-0220-1
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