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On the equations \(u_ t + \nabla \cdot F(u) = 0\) and \(u_ t + \nabla \cdot F(u) = \nu\Delta u\). (English) Zbl 0185.34601

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[1] Edward Conway and Joel Smoller, Clobal solutions of the Cauchy problem for quasi-linear first-order equations in several space variables, Comm. Pure Appl. Math. 19 (1966), 95 – 105. · Zbl 0138.34701 · doi:10.1002/cpa.3160190107 · doi.org
[2] O. A. Oleń≠nik, Discontinuous solutions of non-linear differential equations, Uspehi Mat. Nauk (N.S.) 12 (1957), no. 3(75), 3 – 73 (Russian).
[3] A. I. Vol\(^{\prime}\)pert, Spaces \?\? and quasilinear equations, Mat. Sb. (N.S.) 73 (115) (1967), 255 – 302 (Russian).
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