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    Please use this identifier to cite or link to this item: http://tkuir.lib.tku.edu.tw:8080/dspace/handle/987654321/97799


    Title: Convergence and blow-up of solutions for a complex-valued heat equation with a quadratic nonlinearity
    Authors: Guo, Jong-Shenq;Hirokazu Ninomiya;Masahiko Shimojo;Eiji Yanagida
    Contributors: 淡江大學數學學系
    Keywords: Complex-valued heat equation;parabolic system;convergence;blow-up
    Date: 2013-05-01
    Issue Date: 2014-04-21 21:34:52 (UTC+8)
    Publisher: Providence: American Mathematical Society
    Abstract: 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.
    Relation: Transactions of the American Mathematical Society 365(5), pp.2447-2467
    DOI: 10.1090/S0002-9947-2012-05797-7
    Appears in Collections:[數學學系暨研究所] 期刊論文

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