Asymptotically Self-similar Solution for the Convection-Diffusion Equation

摘要

We study the Cauchy problem for the convection-diffusion equation, which describes physical phenomena where particles, energy, or other physical quantities are transferred inside a physical system due to diffusion and convection processes. For a > 2, we show the continuous dependence upon the initial data. Moreover, asymptotically self-similar global solutions are investigated with nonhomogeneous initial date.