60 citations · 72 across the 10 of their papers we have counts for
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Nonnegative solutions for a long-wave unstable thin film equation with convection
Marina Chugunova, M. C. Pugh, R. M. Taranets
We consider a nonlinear 4th-order degenerate parabolic partial differential equation that arises in modelling the dynamics of an incompressible thin liquid film on the outer surfac…
Technical report on a long-wave unstable thin film equation with convection
Marina Chugunova, M. C. Pugh, R. M. Taranets
In this technical report, we consider a nonlinear 4th-order degenerate parabolic partial differential equation that arises in modelling the dynamics of an incompressible thin liqui…
Heteroclinic orbits, mobility parameters and stability for thin film type equations
R. S. Laugesen, M. C. Pugh
We study numerically the phase space of the evolution equation h_t = -(h^n h_{xxx})_x - B (h^m h_x)_x . Here h(x,t) is nonnegative, n>0 and m is real, and the Bond number B is posi…
Energy levels of steady states for thin film type equations
R. S. Laugesen, M. C. Pugh
We study the phase space of the evolution equation h_t = -(f(h) h_{xxx})_x - (g(h) h_x)_x by means of a dissipated energy (a Liapunov function). Here h(x,t) is nonnegative, and at…