Some relations between nonexpansive and order preserving mappings. (English) Zbl 0449.47059


47H07 Monotone and positive operators on ordered Banach spaces or other ordered topological vector spaces
35F25 Initial value problems for nonlinear first-order PDEs
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
Full Text: DOI


[1] Haïm Brézis and Walter A. Strauss, Semi-linear second-order elliptic equations in \?\textonesuperior , J. Math. Soc. Japan 25 (1973), 565 – 590. · Zbl 0278.35041 · doi:10.2969/jmsj/02540565
[2] Michael G. Crandall and Andrew Majda, Monotone difference approximations for scalar conservation laws, Math. Comp. 34 (1980), no. 149, 1 – 21. · Zbl 0423.65052
[3] A. Douglis, Lectures on discontinuous solutions of first order nonlinear partial differential equations in several space variables, North British Symposium on Partial Differential Equations, 1972. · Zbl 0228.35020
[4] Ignace I. Kolodner, On the Carleman’s model for the Boltzmann equation and its generalizations, Ann. Mat. Pura Appl. (4) 63 (1963), 11 – 32. · Zbl 0158.11201 · doi:10.1007/BF02412176
[5] S. N. Kružkov, Generalized solutions of nonlinear equations of the first order with several variables. I, Mat. Sb. (N.S.) 70 (112) (1966), 394 – 415 (Russian).
[6] Thomas G. Kurtz, Convergence of sequences of semigroups of nonlinear operators with an application to gas kinetics, Trans. Amer. Math. Soc. 186 (1973), 259 – 272 (1974). · Zbl 0275.47047
[7] Michel Pierre, Un théorème général de génération de semi-groupes non linéaires, Israel J. Math. 23 (1976), no. 3-4, 189 – 199. · Zbl 0343.34050 · doi:10.1007/BF02761799
[8] G. Pólya and G. Szegö, Isoperimetric Inequalities in Mathematical Physics, Annals of Mathematics Studies, no. 27, Princeton University Press, Princeton, N. J., 1951. · Zbl 0044.38301
[9] Elias M. Stein and Guido Weiss, Introduction to Fourier analysis on Euclidean spaces, Princeton University Press, Princeton, N.J., 1971. Princeton Mathematical Series, No. 32. · Zbl 0232.42007
[10] Michael B. Tamburro, The evolution operator solution of the Cauchy problem for the Hamilton-Jacobi equation, Israel J. Math. 26 (1977), no. 3-4, 232 – 264. · Zbl 0357.35017 · doi:10.1007/BF03007645
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.