Global existence of entropy weak solutions and partial uniqueness are established for scalar balance laws with singular nonlocal sources, plus an Oleinik-type estimate and a local smoothness/wave-breaking criterion.
Kato, The Cauchy problem for quasi-linear symmetric hyperbolic systems,Arch
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On scalar nonlinear balance laws with singular nonlocal sources
Global existence of entropy weak solutions and partial uniqueness are established for scalar balance laws with singular nonlocal sources, plus an Oleinik-type estimate and a local smoothness/wave-breaking criterion.