Abstract

YAN, JIN; CHENG, ZHIXIN  and  TAO, MING. Conservation laws I: viscosity solutions. Rev.colomb.mat. [online]. 2007, vol.41, n.1, pp.81-90. ISSN 0034-7426.

In this paper we use the Brouwer-Schauder's fixed point theorem to obtain the existence of local smooth viscosity solutions of the Cauchy problem for the parabolic system with the bounded measurable initial data Then based on the local existence and the maximum principle, we get the existence of global smooth solutions for two special systems, one related to the hyperbolic system of quadratic flux and the other related to the LeRoux system.

Keywords : Hyperbolic conservation laws; viscosity solution; Cauchy problem; a priori estimate.

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