论文标题
在具有空间依赖系数的高阶双曲方程上
On higher order hyperbolic equations with space-dependent coefficients: $C^\infty$ well-posedness and Levi conditions
论文作者
论文摘要
本文有助于对具有多重性的双曲线方程进行更广泛的研究。我们在这里专注于在任何空间维度中具有依赖空间系数的高阶双曲线方程。我们证明，在适当的LEVI条件下，相应的库奇问题的Sobolev适合库奇问题（由于多重性而导致的衍生物丧失）。这些条件在\ cite {o70}中概括了众所周知的Olienik条件，以高于$ 2 $的订单。
This paper contributes to the wider study of hyperbolic equations with multiplicities. We focus here on some classes of higher order hyperbolic equations with space dependent coefficients in any space dimension. We prove Sobolev well-posedness of the corresponding Cauchy problem (with loss of derivatives due to the multiplicities) under suitable Levi conditions on the lower order terms. These conditions generalise the well known Olienik's conditions in \cite{O70} to orders higher than $2$.
