A class of nonlinear, nonhyperbolic systems of conservation laws with well-posed initial value problems

作者：Sever M^*

来源：Journal of Differential Equations, 2002, 180(1): 238-271.

DOI：10.1006/jdeq.2001.4060

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.

• 出版日期2002-3-20