Abstract
With mild restrictions on the initial data, we show well-posedness of the initial value problem for systems of conservation laws in one space variable with real and equal characteristic speeds and a deficiency of one corresponding eigenvector. The obtained weak solutions assume values as Borel measures at each time after a smooth solution ceases to exist. The concept of entropy density–flux functions is extended to such systems. Finally, we show that systems with well-posed initial value problems, admitting weak solutions of this type, necessarily satisfy these structural assumptions.
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