摘要
讨论以下三维广义Ginzburg Landau方程的初边值问题ut =-a1Δ4u+a2 Δ2 u+Δ2 g(u) +G(u) ,u｜ Ω =0 ,Δ2 u｜ Ω =0 ,u(x ,0 ) =u0 (x) .首先 ,应用Galerkin方法和紧致性定理证明上述问题整体广义解和整体古典解的存在性和惟一性 ;其次 ,给出了解爆破的充分条件 ;最后 ,证明上述问题的广义解和古典解当t→ +∞时依L2 范数趋于零 .
The following initial boundary value problem is discussed u_t=-a_1 Δ 4 u+a_2 Δ 2 u+ Δ 2 g(u)+G(u),u|_ Ω =0,Δ 2 u|_ Ω =0,u(x,0)=u_0(x). First,the existence of the global generalized and classical solution to the above problem are proved by use of the Galerkin method and compactness theorem.Second,the sufficient conditions of blow up of the solution are given.Third,it is proved that the solution tends to zero in L_2 space as t approaches to infinity.
出处
《郑州大学学报（理学版）》
CAS
2003年第4期1-6,共6页
Journal of Zhengzhou University:Natural Science Edition
基金
国家自然科学基金资助项目
编号 10 0 710 74
河南省自然科学基金资助项目
