| Abstract: |
| Systems for parabolic-hyperbolic conservation laws are interesting research object in the sense of mathematics and applications. In a mathematical point of view, the systems have both properties of hyperbolic equations and those of parabolic equations. Therefore, it has discontinuous solutions in general. From this, the unified well-posedness theory is not given. In application point of view, the systems can be applied to many mathematical models (fluid dynamics, traffic flow, aggregation phenomena, crowd dynamics and so on).
In this talk, we formulate initial value problems for the systems and discuss solvability of the problem. |
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