Local solution of Cauchy problem for nonlinear hyperbolic systems in Gevrey classes
Local solution of Cauchy problem for nonlinear hyperbolic systems in Gevrey classes
复制标题
Gevrey类非线性双曲系统柯西问题的局部解
DOI：
10.14492/hokmj/1525852966
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发表时间：
1983
影响因子：
0.5
通讯作者：
K. Kajitani
中科院分区：
文献类型：
--
作者：
K. Kajitani
Leray-Ohya [7] （c. f.[8]）研究了Gevrey类中非线性双曲型方程的Cauchy问题。他们假设特征是恒定的多重性或平滑的。在本文中，我们将取消这一限制。我们考虑以下方程的未知数u (x) = (u_ {1} (x) \ cdots u_ {N} (x)), x =(间的{0},间{1 ^ {}},\ cdots间{N}) =(间的{0},d)在R ^ \ {N + 1},(0。1) f{我}(x, D ^ {M_{我}}u (x)) = 0 \ω,i = 1, \ cdots, N,
Introduction The Cauchy problem for nonlinear hyperbolic equations in Gevrey classes was studies by Leray-Ohya [7] (c. f. [8]) . They assume that the characteristics are of constant multiplicity or smooth. In this paper we shall remove this restriction. We consider the following equations for the unknowns u(x)=(u_{1}(x), \cdots , u_{N}(x)) , x=(x_{0}, x_{1^{ }},\cdots, x_{n})=(x_{0}, d)\in R^{n+1}, (0. 1) F_{i}(x, D^{M_{i}}u(x))=0 in \Omega , i=1, \cdots , N ,