We study the well-posedness of a hyperbolic characteristic initial boundary value problem with Lipschitz continuous coefficients. Assuming more general boundary assumptions than those of maximally dissipativeness, we deal with a Friedrichs symmetrizable system of first order satisfying a minimal structure boundary condition, the so-called Uniform Kreiss–Lopatinskii Condition. We show that a semi-group estimate holds, leading to the proof of the \(L^{2}\) well-posedness of the initial boundary value problem, provided that the source data of the interior is only \(L^{1}([0,T],L^{2}(\varOmega )),\) with the aid of the paradifferential calculus.

我们研究具有Lipschitz连续系数的双曲特征初始边界值问题的适定性。假设比最大耗散性更普遍的边界假设，我们处理的是满足最小结构边界条件的一阶Friedrichs可对称系统，即所谓的均匀Kreiss-Lopatinskii条件。我们证明了半群估计成立，只要内部的源数据仅为\ {L ^ {，就可以证明初始边界值问题的\（L ^ {2} \）适定性。1}（[0，T]，L ^ {2}（\ varOmega））\）借助超微积分。