| Abstract: |
| In this talk, we consider initial-boundary value problems for the one-dimensional isentropic Euler system in the half-space, focusing on both inflow and outflow problems. We prove that small BV solutions in the subsonic region are unique and stable within a wild class of weak solutions satisfying the so-called strong trace property. In particular, we establish quantitative H\older-type stability estimates in the $L^2$ norm. While the small BV solutions, being in the subsonic region, are associated with non-characteristic boundaries, the wild solutions admit characteristic boundaries. Our analysis is based on the method of $a$-contraction with shifts, although the stability results do not depend on the shift. This talk is based on a joint work with Moon-Jin Kang, Jiayun Meng, and Alexis Vasseur. |
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