A Class Of Two-component Dullin-Gottwald-Holm Correction Equations Solutions Blow

This paper mainly deals with the wave breaking phenomenon of a modified two-component DGH equation in the following formWhere the variable u denotes the velocity field, and ρ=(1-(?)2x)(ρ-ρ0), where ρo is taken to be a constant.By discussing the fundamental solutions of the linear DGH equation with dispersion, in this paper, we shall construct the modified two-component DGH equation, and then we consider two blow-up situations:one is blow-up criteria in non-periodic case; the other is blow-up criteria in periodic case.When γ=A, if mo(x)=uo(x)-uqxx(x) in the model (0.2) satisfies the following initial condition and we can obtain the main blow-up results in non-periodic case.Different from the non-periodic case, the function u(x,t) satisfies u(x,t)=u(x+1,t) in periodic case. We introduce the Green function of the operator (1-(?)2x)-1in the following form where [x] denotes the integer part of x. By disscussing the properties of the function p(x), for any f∈L2(S), the operator (1-(?)2x)-1can be expressed as then we get some blow-up results in periodic case.