Publications [#353091] of Thomas P. Witelski

Papers Published

1. Ji, H; Witelski, T, Steady states and dynamics of a thin-film-type equation with non-conserved mass, European Journal of Applied Mathematics, vol. 31 no. 6 (December, 2020), pp. 968-1001, Cambridge University Press (CUP) [doi]
   (last updated on 2024/04/19)

   Abstract:
   We study the steady states and dynamics of a thin-film-type equation with non-conserved mass in one dimension. The evolution equation is a non-linear fourth-order degenerate parabolic partial differential equation (PDE) motivated by a model of volatile viscous fluid films allowing for condensation or evaporation. We show that by changing the sign of the non-conserved flux and breaking from a gradient flow structure, the problem can exhibit novel behaviours including having two distinct classes of co-existing steady-state solutions. Detailed analysis of the bifurcation structure for these steady states and their stability reveals several possibilities for the dynamics. For some parameter regimes, solutions can lead to finite-time rupture singularities. Interestingly, we also show that a finite-amplitude limit cycle can occur as a singular perturbation in the nearly conserved limit.