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The evolution operator solution of the Cauchy problem for the Hamilton- Jacobi equation. (English) Zbl 0357.35017


MSC:

35F25 Initial value problems for nonlinear first-order PDEs
35D05 Existence of generalized solutions of PDE (MSC2000)
35J60 Nonlinear elliptic equations
47H05 Monotone operators and generalizations
70H20 Hamilton-Jacobi equations in mechanics
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References:

[1] Belova, M. M., On bounded solutions of nonlinear differential equations of second order, Mat. Sb., 56, 98, 469-503 (1962) · Zbl 0105.29202
[2] B. C. Burch,A semigroup treatment of the Hamilton-Jacobi equation in several space variables (to be published). · Zbl 0301.35013
[3] Crandall, M.; Pazy, M., Nonlinear evolution equations in Banach spaces, Israel J. Math., 11, 57-94 (1972) · Zbl 0249.34049 · doi:10.1007/BF02761448
[4] M. Crandall,UCLA Lecture Notes for Math. 285, Spring 1974.
[5] M. A. Krasnoselski,Topological Methods in the Theory of Nonlinear Integral Equations, Pergamon, 1964, p. 20. · Zbl 0111.30303
[6] Kruzkov, S. N., Generalized solutions of first order nonlinear equations in several independent variables, Mat. Sb., 70, 112, 394-415 (1966) · Zbl 0152.09502
[7] G. N. Polozhiy,Equations of Mathematical Physics, Hayden, 1967, pp. 111-114.
[8] E. M. Stein,Singular Integrals and Differentiability Properties of Functions, Princeton, 1970, pp. 130-133. · Zbl 0207.13501
[9] M. B. Tamburro,On the Semigroup Solution of a Hamilton-Jacobi Type Equation, Ph.D. dissertation UCLA, August, 1974.
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