Convergence and blow-up of solutions for a complex-valued heat equation with a quadratic nonlinearity
學年 101
學期 2
出版（發表）日期 2013-05-01
作品名稱 Convergence and blow-up of solutions for a complex-valued heat equation with a quadratic nonlinearity
作品名稱（其他語言）
著者 Guo, Jong-Shenq; Hirokazu Ninomiya; Masahiko Shimojo; Eiji Yanagida
單位 淡江大學數學學系
出版者 Providence: American Mathematical Society
著錄名稱、卷期、頁數 Transactions of the American Mathematical Society 365(5), pp.2447-2467
摘要 This paper is concerned with 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 data 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 solutions with nontrivial imaginary parts that blow up simultaneously. Finally, we consider the case of asymptotically constant initial data and show that, depending on the limit, the solution blows up nonsimultaneously at space infinity or exists globally in time and converges to the trivial steady state.
關鍵字 Complex-valued heat equation; parabolic system; convergence; blow-up
語言 en_US
ISSN 0002-9947
期刊性質 國外
收錄於 SCI
產學合作
通訊作者 Masahiko Shimojo
審稿制度 是
國別 USA
公開徵稿
出版型式 ,紙本
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