On global solution of nonlinear hyperbolic equations
On global solution of nonlinear hyperbolic equations
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DOI：
10.1007/bf00250942
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发表时间：
1968
影响因子：
2.5
通讯作者：
D. Sattinger
中科院分区：
文献类型：
--
作者：
D. Sattinger
K (u)=~ 89 J (u)=~{89(0.4) 分别，其中F是f的反导数：F,= f。假设 J 在 u= Uo (X) 处有局部最小值。然后，与具有有限自由度的机械系统的势函数的局部最小值类比，我们可以想象一个位势井 W 位于函数空间中 u= Uo 处。如果 U 位于 W 中并且初始数据的总能量小于 W 的深度，则我们期望 (0.1)-(0.3) 具有全局解。
K (u)=~ 89 J (u)=~{89(0.4) respectively, where F is an antiderivative of f: F,= f. Suppose that J has a local minimum at u= Uo (X). Then, in analogy with the local minimum of a potential function for a mechanical system with a finite number of degrees of freedom, we may imagine a potential well W situated at u= Uo in function space. If U lies in W and if the total energy of the initial data is less than the depth of W then we expect that (0.1)-(0.3) has a global solution.