On the stability of traveling wave solutions to thin-film and long-wave models for film flows inside a tube
نویسندگان
چکیده
منابع مشابه
Notes on Blowup and Long Wave Unstable Thin Film Equations
(1) ut = −(uuxxx)x − (uux)x. This is the one dimensional version of ut = −∇ · (f(u)∇∆u)−∇ · (g(u)∇u), with f(u) = un and g(u) = un. Such equations have been used to model the dynamics of a thin film of viscous liquid spreading on a flat solid surface. The air/liquid interface is at height z = u(x, y, t) ≥ 0 and the liquid/solid interface is at z = 0. The one dimensional equation (1) applies if ...
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Hocherman and Rosenau conjectured that long-wave unstable Cahn-Hilliard-type interface models develop finite-time singularities when the nonlinearity in the destabilizing term grows faster at large amplitudes than the nonlinearity in the stabilizing term (Phys. D 67, 1993, pp. 113–125). We consider this conjecture for a class of equations, often used to model thin films in a lubrication context...
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ژورنال
عنوان ژورنال: Physica D: Nonlinear Phenomena
سال: 2021
ISSN: 0167-2789
DOI: 10.1016/j.physd.2020.132750