Acta mathematica scientia,Series A ›› 2016, Vol. 36 ›› Issue (6): 1186-1195.

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Blow up and Lifespan Estimates for Initial Boundary Value Problem of Semilinear Schrödinger Equations on Half-Life

Geng Jinbo1, Yang Zhenzhen1, Lai Ning-An2   

  1. 1. Department of Mathematics, Zhejiang Normal University, Zhejiang Jinhua 321004;
    2. Department of Mathematics, Lishui University, Zhejiang Lishui 323000
  • Received:2016-05-07 Revised:2016-09-28 Online:2016-12-26 Published:2016-12-26
  • Supported by:

    Supported by the NSFC (11501273) and the Natural Science Foundation of Zhejiang Province (LQ13A010013,LY14A010010,LY14A010005)

Abstract:

In this paper, we consider the initial boundary value problem of semilinear Schrödinger equation on half-line. Blow up result will be established, assuming the power of the nonlinear term satisfying 1 < p≤2. Furthermore, we obtain the upper bound of the lifespan in the case 1 < p < 2. The proof is based on a contradiction argument, by constructing a special test function.

Key words: Semilinear Schrödinger equation, Blow up, Lifespan

CLC Number: 

  • O212.62
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