The existence of the global solutions to semilinear wave equations with a class of cubic nonlinearities in 2-dimensional space
The existence of the global solutions to semilinear wave equations with a class of cubic nonlinearities in 2-dimensional space
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DOI：
10.14492/hokmj/1249046363
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发表时间：
2008-11
影响因子：
0.5
通讯作者：
A. Hoshiga
中科院分区：
文献类型：
--
作者：
A. Hoshiga
本文研究二维空间中具有小初值的半线性波动方程的柯西问题。当非线性项为三次时，一般不能期望光滑解的整体存在性。然而，Godin [1]证明，如果非线性项具有零形式，则解整体存在。在本文中，我们将显示的整体可解性的其他类型的非线性不具有零形式。
This paper deals with the Cauchy problem of the semilinear wave equation with a small initial data in 2-dimensional space. When the nonlinearity is cubic, we can not expect the global existence of smooth solutions, in general. However, Godin [1] showed that if the nonlinearity has the null-form, the solution exists globally. In this paper, we will show the global solvability for the other type of nonlinearities which does not have null-form.