George Tang

Metastability refers to a phenomenon in which a system rapidly approaches a temporary state, remains near it for a long time, and only later moves toward its final state. In this project, we investigate metastable behavior in the Burgers equation. Using the Cole–Hopf transformation, we study the evolution of solutions arising from step initial condition, corresponding to the classical Riemann problem, and then extend the analysis to multi-block piecewise constant initial data. We find that these solutions evolve through smoothing and merging processes and, over longer times, approach N-wave-like profiles. These results suggest that N-wave structures naturally arise as metastable intermediate states in the Burgers equation.