Literature Cited
A. V. Bitsadze, “On some problems of mixed type,” Dokl. Akad. Nauk SSSR,70, No. 4, 561–565 (1950).
P. Germain and R. Bader, “Sur le probleme de Tricomi,” C. R. Acad. Sci., Paris,232, No. 6, 463–465 (1951).
K. I. Babenko, “On the theory of equations of mixed type,” Doctoral Dissertation in Physicomathematical Sciences, Moscow State Univ., Moscow (1951).
S. Agmon, L. Nirenberg, and M. Protter, “A maximum principle for a class of hyperbolic equations and applications to equations of mixed elliptic-hyperbolic type,” Commun. Pure Appl. Math.,6, No. 4, 455–470 (1953).
A. F. Fillippov, “On a difference method for solving the Tricomi problem,” Izv. Akad. Nauk SSSR, Ser. Mat.,21, No. 1, 73–88 (1957).
M. E. Lerner, “On a maximum principle for hyperbolic equations and its application to equations of mixed type,” Dokl. Akad. Nauk SSSR,177, No. 6, 1269–1272 (1967).
M. E. Lerner, “On an extremal property of solutions of a class of hyperbolic equations,” Dokl. Akad. Nauk SSSR,184, No. 6, 1281–1283 (1969).
L. I. Kovalenko, “On extremum principle for a generalized solution of an equation of mixed type with lower order terms,” Sib. Mat. Zh.,14, No. 1, 221–228 (1973).
L. I. Kovalenko, “Uniqueness of the generalized solution of the Tricomi problem,” Sib. Mat. Zh.,11, No. 6, 1291–1311 (1970).
M. M. Smirnov, Equations of Mixed Type [in Russian], Nauka, Moscow (1970).
V. I. Smirnov, A Course of Higher Mathematics, Vol. 5, Pergamon Press.
Additional information
Moscow Physicotechnical Institute, Moscow. Translated from Sibirskii Matematicheskii Zhurnal, Vol. 22, No. 1, pp. 100–110, January–February, 1981.
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Kovalenko, L.I. An extremum principle for a generalized solution of equations of hyperbolic and mixed type. Sib Math J 22, 73–81 (1981). https://doi.org/10.1007/BF00968202
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DOI: https://doi.org/10.1007/BF00968202