分块均匀介质中Maxwell-Ohm方程组的Cauchy问题

Cauchy Problem for the Maxwell-Ohm System with Piecewise Constant Coefficients

在石油测井模型中,我们遇到一类具有间断系数的Maxwell-Ohm方程组的问题。本文讨论其中有代表性的一类问题—即具有分块常系数和交界面条件的Maxwell-Ohm方程组的Cauchy问题。通过研究该问题所对应的Sobolev空间的性质,并应用算子半群的方法给出该问题解的存在唯一性。

In the mathematical model of a well logging, we confront with a problem of the Maxwell- Ohm system which has discontinuous coefficients. In this paper, we study a typical form of this problem-the Cauchy problem for the Maxwell-Ohm system with piecewise constant coefficients. After studying properties of the relevant Sobolev space, we prove the well-posedness of this problem by means of the theory on the semi-group of operators.