Existence of solutions for a scalar conservation law with a flux of low regularity

We prove existence of solutions to Cauchy problem for scalar conservation laws with non-degenerate discontinuous flux $$ \partial_t u+ \hbox{div}f(t,\mathbf{x},u)=s(t,\mathbf{x},u), \quad t\geq 0, \mathbf{x}\in \mathbb{R}^d, $$ where for every $(t,\mathbf{x})\in \mathbb{R}^+\times \mathbb{R}$,...

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Bibliographic Details
Main Authors: Martin Lazar, Darko Mitrovic
Format: Article
Published: Texas State University 2016-12-01
Series:Electronic Journal of Differential Equations
Online Access:http://ejde.math.txstate.edu/Volumes/2016/325/abstr.html