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IMA Journal of Applied Mathematics Advance Access originally published online on August 19, 2009
IMA Journal of Applied Mathematics 2009 74(5):726-740; doi:10.1093/imamat/hxp024
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© The Author 2009. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

The Cauchy problem for coupled IMBq equations

Shubin Wang{dagger}

Department of Mathematics, Zhengzhou University, Zhengzhou 450001, China

Meiling Li

Department of Mathematics, Lanzhou Longqiao College, Lanzhou 730101, China

{dagger} Email: wangshubin{at}zzu.edu.cn

Received on October 16, 2008; Revision received March 15, 2009. Accepted on July 22, 2009

In this paper, we study the Cauchy problem associated with two coupled IMBq equations. Under the assumptions for non-linear terms and initial data, we prove the existence and uniqueness of the global solution and give sufficient conditions of blow-up of the solution in finite time by convex methods. This supplements and improves some results by Dè Godefroy (1998, IMA J. Appl. Math., 60, 123–138).

Keywords: coupled IMBq equations; Cauchy problem; local solution; global solution; blow-up.


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