On solutions of the reduced model for the dynamical evolution of contact lines

Dmitry Pelinovsky

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arXiv · 1302.1222

On solutions of the reduced model for the dynamical evolution of contact lines

Dmitry Pelinovsky

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Abstract

We solve the linear advection-diffusion equation with a variable speed on a semi-infinite line. The variable speed is determined by an additional condition at the boundary, which models the dynamics of a contact line of a hydrodynamic flow at a 180 contact angle. We use Laplace transform in spatial coordinate and Green's function for the fourth-order diffusion equation to show local existence of solutions of the initial-value problem associated with the set of over-determining boundary conditions. We also analyze the explicit solution in the case of a constant speed (dropping the additional boundary condition).

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Dmitry Pelinovsky. 2013-02-05. On solutions of the reduced model for the dynamical evolution of contact lines. https://arxiv.org/abs/1302.1222

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