The discontinuous initial value problem of a reacting gas flow
HTML articles powered by AMS MathViewer
- by Lung An Ying and Ching Hua Wang PDF
- Trans. Amer. Math. Soc. 266 (1981), 361-387 Request permission
Abstract:
We show that the local solvability of the solution of a reacting gas flow system $(1.1) - (1.4)$ with initial values $(1.5)$, which has a large jump at the point $x’ = 0$ and the structure of the solution near the origin $(0,0)$ are identical to those of the Riemann problem of the homogeneous system corresponding to the Cauchy problem $(1.1) - (1.5)$.References
-
F. A. Williams, Combustion theory, Addison-Wesley, Reading, Mass., 1965.
- K. O. Friedrichs, Nonlinear hyperbolic differential equations for functions of two independent variables, Amer. J. Math. 70 (1948), 555–589. MR 25659, DOI 10.2307/2372200
- Richard Courant and Peter Lax, On nonlinear partial differential equations with two independent variables, Comm. Pure Appl. Math. 2 (1949), 255–273. MR 33443, DOI 10.1002/cpa.3160020206
- Avron Douglis, Some existence theorems for hyperbolic systems of partial differential equations in two independent variables, Comm. Pure Appl. Math. 5 (1952), 119–154. MR 52666, DOI 10.1002/cpa.3160050202
- Philip Hartman and Aurel Wintner, On hyperbolic partial differential equations, Amer. J. Math. 74 (1952), 834–864. MR 51413, DOI 10.2307/2372229
- Peter D. Lax, Nonlinear hyperbolic equations, Comm. Pure Appl. Math. 6 (1953), 231–258. MR 56176, DOI 10.1002/cpa.3160060204
- P. D. Lax, The initial value problem for nonlinear hyperbolic equations in two independent variables, Contributions to the theory of partial differential equations, Annals of Mathematics Studies, no. 33, Princeton University Press, Princeton, N.J., 1954, pp. 211–229. MR 0068093 R. Courant and P. D. Lax, Cauchy problem for nonlinear hyperbolic differential equations in two independent variables, Ann. Mat. Pura Appl. (4) 40 (1955). Wang Row-Hwai and Wuu Jwo-Chun, On mixed boundary value problem for quasilinear hyperbolic system of partial differential equation in two independent variables, Acta Sci. Natur. Univ. Kirin 2 (1963), 459-502. (Chinese) Gu Chao-Hao, Lee Da-Tsin and Ho Zon-Yi, The Cauchy problem of quasilinear hyperbolic system with disontinuous initial values. I, II, Acta Math. Sinica 11 (1961), 314-329; III, Ibid. 12 (1963), 132-143. B. Roždestvenskiĭ and N. Yanenko, The quasilinear systems of equations and their applications to gas dynamics, "Nauka", Moscow, 1968, pp. 538-560. Lee Da-Tsin and Yu Wen-Tzu, Some existence theorems for quasilinear hyperbolic systems of partial differential equations in two independent variables. I: Typical boundary value problems, Sci. Sinica 13 (1964), 529-549; II: Typical boundary problems of functional form and typical free boundary problems, Sci. Sinica 13 (1964), 551-562; III: General boundary value problems and general free boundary problems, Sci. Sinica 14 (1965), 1065-1067.
- Da Qian Li and Wen Ci Yu, Local solvability of the boundary value problems for quasilinear hyperbolic systems, Sci. Sinica 23 (1980), no. 11, 1357–1367. MR 615212, DOI 10.5873/nihonnoshingaku.1963.132
Additional Information
- © Copyright 1981 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 266 (1981), 361-387
- MSC: Primary 35L67; Secondary 80A30
- DOI: https://doi.org/10.1090/S0002-9947-1981-0617539-9
- MathSciNet review: 617539