On global solvability of initial value problem for hyperbolic Monge–Ampère equations and systems
Tóm tắt
The communication concerns a theory of global solvability of initial value problem for nonlinear hyperbolic equations with two independent variables that is an immediate analog of a theory of global solvability of ordinary differential equations.
Tài liệu tham khảo
R. Courant, Methods of Mathematical Physics, Vol. 2: Partial Differential Equations (Interscience, New York, 1962; Moscow, Mir, 1964).
V. V. Lychagin, Russ. Math. 36 (5), 38–51 (1992).
B. L. Roždestvenskii and N. N. Janenko, Systems of Quasilinear Equations and Their Applications to Gas Dynamics (Nauka, Moscow, 1978; Am. Math. Soc., Providence, 1983).
S. J. Bilčev, Izv. Vyssh. Uchebn. Zaved. Mat., No. 3, 14–21 (1970).
A. M. Vasil’ev, Theory of Differential-Geometric Structures (Mosk. Gos. Univ., Moscow, 1987) [in Russian].
P. D. Lax, J. Math. Phys. 5 (5), 611–613 (1964).
N. J. Zabusky, J. Math. Phys. 3 (5), 1028–1039 (1962).
P. Hartman, Ordinary Differential Equations (Wiley, New York, 1964; Mir, Moscow, 1970).
V. V. Kushner, V. V. Lychagin, and V. N. Rubtsov, Contact Geometry and Nonlinear Differential Equations (Cambridge Univ. Press, Cambridge, 2007).