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

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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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      Most cited references 2

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      The Rolling Motion of A Viscous Fluid On and Off a Rigid Surface

       W. Timson,  D. Benney (1980)
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        The moving contact line with a 180° advancing contact angle

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          Author and article information

          Journal
          1302.1222

          Analysis, Thermal physics & Statistical mechanics

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