论文标题
在波动方程上具有多重性和依赖空间的不规则系数
On the wave equation with multiplicities and space-dependent irregular coefficients
论文作者
论文摘要
在本文中，我们研究了具有多重性和空间依赖性不规则系数的波方程的Cauchy问题的良好性。如\ cite {gr：14}为了给出有意义的解决方案的概念，我们采用了非常弱的解决方案的概念，这些构建基于通过Mollifiers的参数依赖性正则化。我们证明，即使有分布系数，我们的库奇问题也存在非常弱的解决方案，并且在系数平滑时会收敛到经典的解决方案。在某些启发性的例子中，在本文的结尾研究了对非常薄弱解决方案的软体动物的依赖。
In this paper we study the well-posedness of the Cauchy problem for a wave equation with multiplicities and space-dependent irregular coefficients. As in \cite{GR:14} in order to give a meaningful notion of solution, we employ the notion of very weak solution, which construction is based on a parameter dependent regularisation of the coefficients via mollifiers. We prove that, even with distributional coefficients, a very weak solution exists for our Cauchy problem and it converges to the classical one when the coefficients are smooth. The dependence on the mollifiers of very weak solutions is investigated at the end of the paper in some instructive examples.
