Classical solutions to the scalar conservation law with discontinuous initial data
Tom 131 / 2013
Colloquium Mathematicum 131 (2013), 1-12 MSC: Primary 35N05. DOI: 10.4064/cm131-1-1
Sufficient and necessary conditions for the existence and uniqueness of classical solutions to the Cauchy problem for the scalar conservation law are found in the class of discontinuous initial data and non-convex flux function. Regularity of rarefaction waves starting from discontinuous initial data and their dependence on the flux function are investigated and illustrated in a few examples.