A L Bertozzi et al 2001 Nonlinearity 14 1569 doi:10.1088/0951-7715/14/6/309
A L Bertozzi1,2, G Grün3 and T P Witelski1
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Under the influence of long-range attractive and short-range repulsive forces, thin liquid films rupture and form complex dewetting patterns. This paper studies this phenomenon in one space dimension within the framework of fourth-order degenerate parabolic equations of lubrication type. We derive the global structure of the bifurcation diagram for steady-state solutions. A stability analysis of the solution branches and numerical simulations suggest coarsening occurs. Furthermore, we study the behaviour of solutions in the limit that short-range repulsive forces are neglected. Both asymptotic analysis and numerical experiments show that this limit can concentrate mass in δ-distributions.
35G25 Initial value problems for nonlinear higher-order PDE, nonlinear evolution equations
Soft matter, liquids and polymers
Issue 6 (November 2001)
Received 10 August 2000, in final form 3 May 2001
Published 21 September 2001
A L Bertozzi et al 2001 Nonlinearity 14 1569
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