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The Cauchy problem for a nonlinear first order partial differential equation. (English) Zbl 0172.13901


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[1] Bellman, R, Dynamic programming, (1957), Princeton · Zbl 0077.13605
[2] Conway, E.D; Hopf, E, Hamilton’s theory and generalized solutions of the Hamilton-Jacobi equation, J. math. mech., 13, 939-986, (1964) · Zbl 0178.11002
[3] {\scDonsker, M.}, An application of function space integrals to a nonlinear equation. To appear.
[4] Dynkin, E.B, Markov processes, (1965), Springer Berlin, [English translation] · Zbl 0132.37901
[5] Federer, H, Two theorems in geometric measure theory, Bull. am. math. soc., 72, 719, (1966) · Zbl 0147.31502
[6] Fleming, W.H, Some Markovian optimization problems, J. math. mech., 12, No. 1, 131-140, (1963) · Zbl 0128.37902
[7] Fleming, W.H, The Cauchy problem for degenerate parabolic equations, J. math. mech., 13, No. 1, 987-1008, (1964) · Zbl 0192.19602
[8] Fleming, W.H, Duality and a priori estimates in Markovian optimization problems, J. math. anal. appl., 16, No. 2, 254-279, (1966) · Zbl 0203.22101
[9] Friedman, A, Partial differential equations of parabolic type, (1964), Prentice Hall Englewood Cliffs · Zbl 0144.34903
[10] Hestenes, M.R, Calculus of variations and optimal control theory, (1966), Wiley New York · Zbl 0173.35703
[11] Hopf, E, The partial differential equation ut + uux = μuxx, Comm. pure appl. math., 3, 201-230, (1950)
[12] Hopf, E, Generalized solutions of nonlinear equations of first order, J. math. mech., 14, 951-972, (1965) · Zbl 0168.35101
[13] Kruzhkov, S.N; Kruzhkov, S.N, The Cauchy problem in the large for certain quasilinear systems of first-order with several variables, Dokl. akad. nauk., Soviet math., 5, 493-496, (1964) · Zbl 0138.34702
[14] Oleǐnik, O.A; Kruzhkov, S.N, Quasilinear parabolic equations of second order with many independent variables, Uspekhi mat. nauk., 16, No. 5, 115-155, (1961)
[15] Kuznetzov, N.N; Šiškin, A.A, On a many dimensional problem in the theory of quasilinear equations, Z. vyčisl. mat. i mat. fiz., 4, No. 4, 192-205, (1964), suppl.
[16] Lax, P.D, Hyperbolic systems of conservation laws II, Comm. pure appl. math., 10, 537-566, (1957) · Zbl 0081.08803
[17] Oleǐnik, O.A; Oleǐnik, O.A, Discontinuous solutions of non-linear differential equations, uspekhi mat. nauk. (NS), am. math. soc. transl., ser. 2, 26, No. 3, 95-172, (1957), English transl. · Zbl 0131.31803
[18] Varadhan, S.R.S, Asymptotic probabilities and differential equations, Comm. pure appl. math., 19, 261-286, (1966) · Zbl 0147.15503
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