References
N. A. Ëltysheva, “To the question of stability of stationary solutions to some hyperbolic systems,” Dokl. Akad. Nauk SSSR,289, No. 1, 30–32 (1986).
N. A. Ëltysheva, “On qualitative properties of solutions to some hyperbolic systems on the plane,” Mat. Sb.,135, No. 2, 186–209 (1988).
T. I. Zelenyak, “On stationary solutions to the mixed problems arising in study of some chemical processes,” Differentsial'nye Uravneniya,2, No. 2, 205–213 (1966).
V. È. Abolinya and A. D. Myshkis, “A. mixed problem for an almost linear hyperbolic system on the plane,” Mat. Sb.,50, No. 4, 423–442 (1960).
V. È. Abolinya and A. D. Myshkis, “On a mixed problem for an almost linear hyperbolic system on the plane,” Uchen. Zap. Latv. Univ.,20, No. 3, 87–104 (1958).
S. K. Godunov, Equations of Mathematical Physics [in Russian], Nauka, Moscow (1979).
J. Rauch and M. Reed, “Jump discontinuities of semilinear, strictly hyperbolic systems in two variables: creation and propagation,” Comm. Math. Phys.,81, No. 2, 203–227 (1981).
J. Rauch and M. Reed, “Nolinear microlocal analysis of semilinear hyperbolic systems in one space dimension,” Duke Math. J.,49, No. 2, 397–475 (1982).
M. Oberguggenberger, “Propagation of singularities for semilinear hyperbolic initial-boundary value problems in one space dimension,” J. Differential Equations,61, No. 1, 1–39 (1986).
K. V. Brushlinskiî, “On the growth of a solution to a mixed problem in the case when the system of eigenfunction is incomplete,” Izv. Akad. Nauk SSSR Ser. Mat.,23, No. 6, 893–912 (1959).
V. S. Sheplev and V. D. Meshcheryakov, “Mathematical modeling of reactors with fluidized bed of a catalyst,” in: Mathematical Modeling of Chemical Reactors [in Russian], Nauka, Novosibirsk, 1984, pp. 44–65.
Additional information
The research is financially supported by the “Russian Universities” program (Grant MM7.8/3H-303-92) and the Russian Foundation for Basic Research (Grant 96-01-01618).
Novosibirsk. Translated fromSibirskiï matematicheskiï Zhurnal, Vol. 38, No. 1, pp. 109–124, January–February, 1997.
Translated by G. V. Dyatlov
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Lavrent'ev, M.M., Lyul'ko, N.A. Increasing smoothness of solutions to some huperbolic problems. Sib Math J 38, 92–105 (1997). https://doi.org/10.1007/BF02674905
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DOI: https://doi.org/10.1007/BF02674905