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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

##### Keywords:
partial differential equations
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##### References:
 [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. Oleĭnik, 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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