On the blow-up phenomenon for a generalized Davey-Stewartson system

Abstract

The blow-up solutions of the Cauchy problem for a generalized Davey-Stewartson system, which models the wave propagation in a bulk medium made of an elastic material with coupled stresses, are investigated. The mass concentration is established for all the blow-up solutions of the system. The profile of the minimal blow-up solutions as t → T (blow-up time) is discussed in detail in terms of the ground state.