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Temple, Blake

Global solution of the Cauchy problem for a class of 2x2 nonstrictly hyperbolic conservation laws. (English) Zbl 0508.76107

Adv. Appl. Math. 3, 335-375 (1982).
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Cited in 1 Review
Cited in 99 Documents

MSC:

76S05 Flows in porous media; filtration; seepage
76T99 Multiphase and multicomponent flows
35K45 Initial value problems for second-order parabolic systems
35K55 Nonlinear parabolic equations
76M99 Basic methods in fluid mechanics

Keywords:

global solution; Cauchy problem; conservation laws; not strictly hyperbolic; Darcy’s law; flow of water and oil; solution of polymer; pumped into reservoir; Riemann problem; weak solution; Glimm difference scheme converges
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\textit{B. Temple}, Adv. Appl. Math. 3, 335--375 (1982; Zbl 0508.76107)
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References:

[1] Glimm, J., Solutions in the large for nonlinear hyperbolic systems of equations, Comm. Pure Appl. Math., 18, 697-715 (1965) · Zbl 0141.28902
[2] E. Isaacson; E. Isaacson
[3] Keyfitz, B.; Kranzer, H., A system of non-strictly hyperbolic conservation laws arising in elasticity theory, Arch. Rat. Mech. Anal., 72 (1980) · Zbl 0434.73019
[4] Lax, P. D., Hyperbolic systems of conservation laws, II, Comm. Pure. Appl. Math, 10, 537-566 (1957) · Zbl 0081.08803
[5] Lax, P. D., Shock waves and entropy, (Zarantonello, E. H., Contributions to Nonlinear Functional Analysis (1971), Academic Press: Academic Press New York), 603-634 · Zbl 0268.35014
[6] D. W. Peaceman; D. W. Peaceman · Zbl 0204.28001
[7] Liu, T. P.; Wang, C. H., On a hyperbolic system of conservation laws which is not strictly hyperbolic, MRC Technical Summary Report 2184 (1981), March
[8] Nishida, T., Global solutions for an initial boundary value problem of a quasilinear hyperbolic system, (Proc. Japan Acad., 44 (1968)), 642-646 · Zbl 0167.10301
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