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The thin film equation with non zero contact angle:A singular perturbation approach
thin film equation non zero contact angle singular perturbation approach
2015/10/15
In this paper we prove the existence of weak solutions for the thin film equation with prescribed non zero contact angle and for a large class of mobility coefficients, in dimension 1. The existence o...
Lyapunov's method proves convergence to equilibrium for a thin film equation
Lyapunov's method proves convergence to equilibrium thin film equation
2010/11/15
The degenerate parabolic equation u_t + [u^3(u_xxx + u_x - sin x)]_x=0 with periodic boundary conditions models the evolution of a thin liquid film on a stationary horizontal cylinder. The equation d...
Local Bifurcation-Branching Analysis of Global and "Blow-up" Patterns for a Fourth-Order Thin Film Equation
Thin film equation local bifurcation analysis source-type and blow-up similarity solutions
2010/12/14
Countable families of global-in-time and blow-up similarity sign-changing patterns of the Cauchy problem for the fourth-order thin film equation (TFE–4) ut = −∇ · (|u|n∇u) in RN × R...
On the energy-minimizing steady states of a thin film equation
energy-minimizing steady states thin film equation
2010/12/9
Steady states of the thin film equation ut + [u3 (uθθθ + 2uθ − sin )]θ = 0 are considered
on the periodic domain = (−, ). The equation defines a generalized gradient flow for an
ene...