Ginzburg-Landau方程的非齐次初边值问题

Inhomogeneous Initial Boundary Value Problem for Generalized Ginzburg-Landau Equations

1.
Department of Mathematics, Foshan University, Foshan, Guangdong 528000, P. R. China;

摘要: 研究具非线性边界条件的一类广义Ginzburg-Landau方程解的整体存在性．推导了Ginzburg-Landau方程的非齐次初边值问题光滑解的几个积分恒等式，由此得到了解的法向导数在边界上的平方模以及解的平方模和导数的平方模估计；通过逼近技巧、先验估计和取极限方法证明了Ginzburg-Landau方程的非齐次初边值问题整体弱解的存在性．
- 广义Ginzburg-Landau方程 /
- 非齐次初边值问题 /
- 弱解 /
- 整体存在性
Abstract: The existence of global weak solution for a class of generalized Ginzburg-Landau equations with an inhomogeneous boundary condition was studied Some integral indentities of smooth solution of inhomogeneous initial boundary value problem of Ginzburg-Landau equations were deduced,by which a priori estimates of the square none on boundary of normal derivative and the square norm of partial derivatives were obtaned Then the existence of global weak solution for an inhomogeneous initial boundary value problem of Ginzburg-Landau equations was proved by the method of approximation technique and a priori estimates and making lirrit.
- generalized Ginzburg-Landau equation /
- inhomogeneous initial boundary value problem /
- weak solution /
- global existence

[1]	Duan J, Holmes P,Titi E S. Global existence theory for a generalized Ginzburg-Landau equation[J].Nonlinearity,1992,5(6):1303—1314. doi: 10.1088/0951-7715/5/6/005
[2]	Duan J,Holmes P.On the Cauchy problem of generalized Ginzburg-Landau equation[J].Nonlinear Anal,TMA,1994,22(8):1033—1040. doi: 10.1016/0362-546X(94)90065-5
[3]	GUO Bo-ling,GAO Hong-jun.Finite dimensional behavior of generalized Ginzburg-Landau equation[J].Progress in Natural Science,1995,5(6):649—610.
[4]	Doering C R,Gibbon J D,Levermore C D.Weak and strong solutions of the complex Ginzburg-Landau equation[J].Phys D,1994，71(3):285—318. doi: 10.1016/0167-2789(94)90150-3
[5]	Bartuccelli M V,Constantin P,Doering C,et al.On the possibility of soft and hard turbulence in the complex Ginzburg-Landau equation[J].Phys D，1990，44(3):421—444. doi: 10.1016/0167-2789(90)90156-J
[6]	Watler Strauss,Charles B U.An inhomogeneous boundary value problem for nonlinear Schrdinger equations[J].J Differential Equations,2001，173(1)：79—91. doi: 10.1006/jdeq.2000.3871
[7]	郭柏灵.粘性消去法和差分格式的粘性[M].北京：科学出版社，1993,26—39.