Abstract
The mixed problem for hyperbolic regularization of conservation laws is studied.
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S. Chapman and T. Cowling, Mathematical Theory of Non-uniform Gases, 3rd. ed., Cambridge Univ.Press, Cambridge (1970).
W. Dreyer and H. Struchtrup, “Heat pulse experiments revisited,” Contin. Mech. Thermodyn., 5, 3–50 (1993).
I. Edelman and S. A. Shapiro, “An analytical approach to the description of fluid injection induced microseismicity in porous rock, Dokl. Earth Sci., 399, No. 8, 1108–1112 (2004).
Chen Gui-Qiang, C. D. Levermore, and Luui Tai-Ping, “Hyperbolic conservation laws with stiff relaxation terms and entropy,” Commun. Pure Appl. Math., XLVII, 787–830 (1994).
H.-O. Kreiss, Initial Boundary Value Problems for Hyperbolic Systems, Uppsala University, Department of Computer Sciences (1969).
C. D. Levermore, “Moment closure hierarchies for kinetic theories,” J. Stat. Phys., 83, 1021–1065 (1996).
I. Müller and T. Ruggeri, Extended Thermodynamics, Springer-Verlag (1993).
V. A. Palin, “On solvability of quadratic matrix equations,” Vestn. MGU (in press).
V. A. Palin and E. V. Radkevich, “The Navier–Stokes approximation and problems of the Chapman–Enskog projection for kinetic equations,” Tr. I. G. Petrovskii Semin., No. 25, 184–225 (2006).
R. Peierls, “Zur kinetischen theorie der warmeleitung in kristallen,” Ann. Phys., 3, 1055 (1929).
E. V. Radkevich, “Irreducible Chapman–Enskog Projections and Navier–Stokes Approximations,” In: Instability in Models Connected with Fluid Flows. II, Int. Math. Ser., 6, 85–151 (2007).
E. V. Radkevich, “Irreducible Chapman–Enskog projections and problems of the Navier–Stokes approximation,” Tr. Mat. Steklov Inst., 250, 219–225 (2005).
E. V. Radkevich, Mathematical Questions of Nonequilibrium Processes [in Russian], “Tamara Rozhkowskaya” Publishing House, White Series, Novosibirsk (2007).
H. Struchtrup and W. Weiss, “Temperature jump and velocity slip in the moment method,” Contin. Mech. Thermodyn., 12, 1–18 (2000).
L. R. Volevich and S. G. Gindikin, Mixed Problem for Partial Differential Equations with Quasihomogeneous Leading Term [in Russian], Editorial URSS, Moscow (1999).
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Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 64, Equations of Mathematical Physics, 2009.
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Zagrebaev, I.V. On the mixed problem for hyperbolic regularizations of conservation laws. J Math Sci 164, 964–975 (2010). https://doi.org/10.1007/s10958-010-9777-4
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DOI: https://doi.org/10.1007/s10958-010-9777-4