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In this paper we will prove the existence of non-negative solutions of the modified lubrication equation with presure boundary condition
where p is a constant. We will show that any sequence
will have a subsequence converging uniformly on
to some function u
(∞) in
We find that if u
(∞)=0 on
, then
If u
0 is even and p > 2, then
are determined by the equations
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