The cauchy problem for a complex-valued heat equation with a quadratic nonlinearity
學年 101
學期 1
發表日期 2012-10-13
作品名稱 The cauchy problem for a complex-valued heat equation with a quadratic nonlinearity
作品名稱（其他語言）
著者 Guo, Jong-Shenq
作品所屬單位 淡江大學數學學系
出版者
會議名稱 第一屆南區微分方程研討會=First Annual Southern Taiwan Workshop on Differential Equations
會議地點 Tainan, Taiwan
摘要 We study the Cauchy problem for a system of parabolic equations which is derived from a complex-valued equation with a quadratic nonlinearity. First we show that if the convex hull of the image of initial datum does not intersect the positive real axis, then the solution exists globally in time and converges to the trivial steady state. Next, on the one dimensional space, we provide some simultaneous blow-up solutions with nontrivial imaginary part. Finally, we consider the case of asymptotically constant initial data and show that, depending on the limit, the solution blows up non-simultaneously at space infinity or exists globally in time and converges to the trivial steady state. This talk is based on a joint work with Ninomiya, Shimojo and Yanagida.
關鍵字
語言 en
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會議性質 國內
校內研討會地點
研討會時間 20121013~20121013
通訊作者
國別 TWN
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機構典藏連結 ( http://tkuir.lib.tku.edu.tw:8080/dspace/handle/987654321/99674 )

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