Piecewise regular solutions to scalar balance laws with singular nonlocal sources
arXiv:2409.01703 · doi:10.1016/j.jde.2024.07.004
Abstract
The present paper establishes a local well-posed result for piecewise regular solutions with single shock of scalar balance laws with singular integral of convolution type kernels. In a neighborhood of the shock curve, a detailed description of the solution is provided for a general class of initial data.