A blow-up problem for a nonlinear heat equation in the complex plane of time
A blow-up problem for a nonlinear heat equation in the complex plane of time
复制标题
复时间平面上非线性热方程的爆炸问题
DOI：
10.1007/s13160-015-0203-7
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发表时间：
2016
期刊：
影响因子：
--
通讯作者：
& M. Shoji
中科院分区：
文献类型：
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作者：
C.-H. Cho;H. Okamoto;& M. Shoji
在复平面上随时间变化对非线性热方程的解进行数值计算，并寻找可能的奇点。事实证明，在复半平面中，其中 表示复数的实部，除了实线上存在的奇点之外，没有奇点。然而，如果我们在黎曼曲面中进一步计算，就会发现新的奇点。与我们的问题相关的某个非线性薛定谔方程也进行了数值计算，并且我们提出了一个猜想，即它在时间上是全局适定的。
Solutions of a nonlinear heat equation are numerically computed in the time variabletlying in the complex plane, and possible singularities are sought. It turns out that in the complex half plane, wheredenotes the real part of a complex number, there is no singularity other than that which exists on the real line. However, if we compute further in the Riemann surface, new singularities are found. A certain nonlinear Schrödinger equation which is associated with our problem is also computed numerically and we propose a conjecture that it is well-posed globally in time.