Solution of a transport equation with discontinuous coefficients. (English) Zbl 1479.35233
Summary: In this article, we study initial and initial-boundary value problems for a non-strictly hyperbolic system whose characteristic speed is not smooth and takes values in \(\{ -1,0,1\}\). We construct an explicit formula for the weak solution. We also study the interaction of waves and the large time asymptotic behavior of a solution for the case when the initial data is periodic with zero mean over the period and also for the case when the initial data has compact support.
MSC:
| 35F61 | Initial-boundary value problems for systems of nonlinear first-order PDEs |
| 35B40 | Asymptotic behavior of solutions to PDEs |
| 35D30 | Weak solutions to PDEs |
| 35L50 | Initial-boundary value problems for first-order hyperbolic systems |
| 35L65 | Hyperbolic conservation laws |
| 35R05 | PDEs with low regular coefficients and/or low regular data |
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