Abstract: The fluidized-bed modeling equation is an important model in the dynamics of two-phase flow. In this paper, we consider the asymptotic stability of the monotone decreasing kink profile solitary-wave solution of the equation. At first, we obtain the first and second derivative estimates of the kink profile solitary-wave solution. Then according to the technical energy estimation and Young inequalities, we overcome the difficulty caused by the complex dissipative term, and establish the uniformly energy estimate for the perturbation of the traveling wave solution. Finally, we prove that the monotone decreasing kink profile solitary-wave solution is asymptotically stable.

Key words: fluidized-bed modeling equation, monotone decreasing kink profile solitary-wave solution, priori energy estimate, Young inequality, asymptotic stability