【摘 要】
：
For any n > 0 we wilt prove the existence of non-negative solution of the thin film equation ut + (|u|nuxxx)x =0 in S1 × (0,∞),S1 =(-1,1),u(X,0) =u0(X) ≥
【机 构】
：
InstituteofMathematics,AcademiaSinica,Taiwan,China
【出 处】
：
International Conference on Nonlinear PDEs and Their Applica
论文部分内容阅读
For any n > 0 we wilt prove the existence of non-negative solution of the thin film equation ut + (|u|nuxxx)x =0 in S1 × (0,∞),S1 =(-1,1),u(X,0) =u0(X) ≥ 0,u0(-1) =u0(1) =1,u0 ∈ H1(S1),with pressure boundary condition u(-1,t) =u(1,t) =1,uxx(-1,t) =uxx(1,t) =p,for all t > 0 where p is a constant in R and the initial value u0 satisfies the condition ∫s1 u20-ndx < ∞for n > 2 and ∫s1 | log u0|dx < ∞ for n =2.We will also prove the large time behaviour of the solution as t → ∞.
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