CHARACTERISTIC BOUNDARY VALUE PROBLEM FOR LINEAR AND NONLINEAR SYMMETRIC HYPERBOLIC SYSTEMS

(1)得到了具有常多重特征边界的线性对称双曲系统初边值问题解的调节定理的最终形式。将“局部”解论证的延拓与已有的结果相结合，得到了一个新的结果。我们现在可以说线性理论完成了。对于拟线性情况，我们的研究结果仍然很差。研究这个问题有很多事情要做。(2)研究了具有强吸收项的非线性扩散方程。我们主要感兴趣的现象，被称为分裂的支持的解决方案。在数学上，这可以看作是一个移动边界问题。我们成功地为这些方程的数值分析构造了一个很好的格式。因此，我们能够找到一个充分的结论，在这个结论下，解的支持发生分裂。

(1) We obtained a final form of the regulatory theorem for solutions to the initial boundary value problem for linear symmetric hyperbolic systems with characteristic boundary of constant multiplicity. Combining the continuation of "local" solution argument with the results which have be established earlier, we reached a new result. We can say now that the linear theory is completed. As for the quasi-linear case, the result of our study is still poor. There are many things to do in studying this problem.(2) We studied the nonlinear diffusion equation with strong absorption term. We have been mainly interested in the phenomenon, called the splitting of the support of solutions. Mathematically, this can be regarded as a moving boundary problem. We succeeded in constructing a good scheme for the numerical analysis of the equations.Thus we were able to find a sufficient conclusion under which the splitting of the support of solutions occurs.