Abstract
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 De Godefroy (1998, IMA J. Appl. Math., 60, 123-138).
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