Abstract: This paper considers the Cauchy problem of the following convection diffusion system
（_v^u）_t+(1)/2(_bu²+2uv^au2+2buv+v2)_x+（_g（u,v）^f(u,v)）=ε(_v^u)_xx, with initial data
（_v^u）|_t=0=(_v0(x)^u₀(x)). A global existence result is established by employing the techniques of F. B. Weissler and the energy method. Here a,b,ε > 0 are constants.

Key words: Inhomogeneous convection diffusion system, global solution, energy method