CHARACTERISTIC BOUNDARY VALUE PROBLEM FOR LINEAR AND NONLINEAR SYMMETRIC HYPERBOLIC SYSTEMS

线性和非线性对称双曲线系统的特征边值问题

基本信息

项目摘要

(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.
(1) 我们得到了具有常重数特征边界的线性对称双曲系统的初始边值问题的调节定理的最终形式。将“局部”解论证的延续与先前建立的结果相结合,我们得出了一个新的结果。现在我们可以说线性理论已经完成。对于拟线性情况,我们的研究结果仍然很差。研究这个问题还有很多工作要做。(2)研究了强吸收项的非线性扩散方程。我们主要对这种称为解决方案支持分裂的现象感兴趣。从数学上讲,这可以看作是一个移动边界问题。我们成功地构建了一个良好的方程数值分析方案。因此,我们能够找到一个充分的结论,在该结论下,解的支持度会发生分裂。

项目成果

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Y.Shizuta: "Strong continuity in time of the solution of the mixed problem for symmetric hyperbolic systems." Nonlinear Analysis. 30/4. 2517-2524 (1996)
Y.Shizuta:“对称双曲系统混合问题的解在时间上具有很强的连续性。”
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M.Ohno & T.Shirota: "On the initial boundary value problem for the linearized MHD equations" Archives for Rational Mechanics and Analysis. (刊行予定).
M.Ohno 和 T.Shirota:“关于线性化 MHD 方程的初始边值问题”Rational Mechanics and Analysis 档案(即将出版)。
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SHIZUTA Yasushi其他文献

SHIZUTA Yasushi的其他文献

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