Abstract: This paper investigated the  estimates of solutions to one-dimensional convection-diffusion equations frac{partial c}{partial t}+ufrac{partial c}{partial x}=Dc_{xx}+c_{xt}-(c{2})_{x}, using Green's function method, frequency decomposition and energy estimates. We found that the decay rate of the solution is the same as that for heat fusion operator

Key words: convection-diffusion equation, estimates, frequency decomposition, Green's function;energy estimates