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Applications of the invariance principle for compact processes. II: Asymptotic behavior of solutions of a hyperbolic conservation law. (English) Zbl 0252.35045

MSC:
35L65 Hyperbolic conservation laws
35B40 Asymptotic behavior of solutions to PDEs
35F10 Initial value problems for linear first-order PDEs
37-XX Dynamical systems and ergodic theory
34C40 Ordinary differential equations and systems on manifolds
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References:
[1] \scC. M. Dafermos, Uniform processes and semicontinuous Liapunov functionals,J. Differential Equations, to appear. · Zbl 0257.35006
[2] Lax, P.D., Hyperbolic systems of conservation laws. II, Comm. pure appl. math., 10, 537-556, (1957) · Zbl 0081.08803
[3] Dafermos, C.M., An invariance principle for compact processes, J. differential equations, 9, 239-252, (1971)
[4] Nemytskiiˇ, V.V.; Stepanov, V.V., Qualitative theory of differential equations, (1960), Princeton University Press Princeton, NJ · Zbl 0089.29502
[5] Hale, J.K., Dynamical systems and stability, J. math. anal. appl., 26, 39-59, (1969) · Zbl 0179.13303
[6] Kruzˇkov, S.N., Generalized solutions of the Cauchy problem in the large for nonlinear equations of first order, Sov. math. dokl., 10, 785-788, (1969)
[7] Hopf, E., On the right weak solution of the Cauchy problem for a quasilinear equation of first order, J. math. mech., 19, 483-487, (1969) · Zbl 0188.16102
[8] \scC. M. Dafermos, Polygonal approximations of solutions of the initial value problem for a conservation law,J. Math. Anal. Appl., to appear. · Zbl 0233.35014
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