Buckmaster equation
From HandWiki
In mathematics, the Buckmaster equation is a second-order nonlinear partial differential equation, named after John D. Buckmaster, who derived the equation in 1977.[1] The equation models the surface of a thin sheet of viscous liquid. The equation was derived earlier by S. H. Smith and by P Smith,[2][3] but these earlier derivations focused on the steady version of the equation. The Buckmaster equation is
- [math]\displaystyle{ u_t = (u^4)_{xx} + \lambda (u^3)_x }[/math]
where [math]\displaystyle{ \lambda }[/math] is a known parameter.
References
- ↑ Buckmaster, J. (1977). Viscous sheets advancing over dry beds. Journal of Fluid Mechanics, 81(4), 735–756.
- ↑ Smith, S. H. (1969). A non-linear analysis of steady surface waves on a thin sheet of viscous liquid flowing down an incline. Journal of Engineering Mathematics, 3(3), 173–179.
- ↑ Smith, P. (1969). On steady long waves on a viscous liquid at small Reynolds number. Journal of Engineering Mathematics, 3(3), 181–187.
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