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4. Ordinary and Partial Differential Equations, Controlled Differential Systems

Piecewise smooth solutions to scalar balance laws with singular source terms

Evangelia Ftaka
NC State University, Raleigh, USA

Abstract:

We will present a local well-posed result for piecewise regular solutions with a single shock of scalar balance laws, with singular integral of convolution type kernels. In a neighborhood of the shock curve, a description of the solution is provided for a general class of initial data.