We will talk about the quasiconvergence and convergence of the solutions to one dimensional parabolic equations. We will consider five problems: parabolic equation in bounded intervals, reaction diffusion equations in the whole line, reaction diffusion equations with free boundaries, porous medium equations with reactions, and reaction diffusion equation in matric graphs. For each of them, we first give the general convergence of bounded solutions to steady states, and then specify the detailed asymptotic behavior for the solutions to bistable reaction diffusion equations.
