关于拟微分算子方程Gevrey解的新探

鹿立江教授在1983年数学学报第1期上研究了一类拟微分算子Cauchy问题的L~2存在性,本文限制非齐次项在Gevrey 函数空间中,得到相应的解也在Gevrey 函数空间中,从而使解更加精确化了;另一方面,本文还继续了Paul R.Wenston 的工作,Paul R.Wenston 在空间L_2([0,T],H_s(R~n))中讨论了一类双曲型拟微分算子方程解的适定性,得到了在Gevrey 函数空间中这类算子的解是存在唯一的.

THE NEW STUDY OF GEVREY SOLUTION FOR PSEUDO-DIFFERENTIAL OPERATOR EQUATION

The Cauchy problem in the Gevrey space is studied to obtain an accurate and precise solution on the basis of the L~2 solutionof Cauchy problem for a kind of pseudo-differential operator equation discussed by Lu Lijiang in 1983.Furthermore,the workby P.R.Wenston is continued as well as the existence and uniqueness of solution to another pseudo-differential operator equa-tion developed well in the Gevrey space.