法向导数 meaning in English
noral derivative
normal derivative
Examples
- This paper uses compare principle to show that there exists at most one of classical solution for ( 1 ) , while the existance of solution is obtained through continuous method . to get the required a priori estimates except the double normal derivatives , we adopt the method in [ 3 ] , and the double normal derivatives on dq are achieved by barrier constructions and applying skill of [ 2 ]
本文用比较原理证明了问题( 1 )至多存在一个古典解，应用连续性方法，得到了问题( 1 )古典解的存在。在得到所需的先验估计时，利用了[ 3 ]中的方法建立了除去边界二阶法向导数外的先验估计，通过构造闸函数，用[ 2 ]中的技巧得到在边界( - Finally , in the third section , by constructing some functional which similar to the conservation law of evolution equation and the technical estimates , we prove that in the inviscid limit the solution of generalized derivative ginzburg - landau equation ( ggl equation ) converges to the solution of derivative nonlinear schrodinger equation correspondently in one - dimension ; the existence of global smooth solution for a class of generalized derivative ginzburg - landau equation are proved in two - dimension , in some special case , we prove that the solution of ggl equation converges to the weak solution of derivative nonlinear schrodinger equation ; in general case , by using some integral identities of solution for generalized ginzburg - landau equations with inhomogeneous boundary condition and the estimates for the l ~ ( 2 ) norm on boundary of normal derivative and h ~ ( 1 ) ' norm of solution , we prove the existence of global weak solution of the inhomogeneous boundary value problem for generalized ginzburg - landau equations
第三部分：在一维情形，我们考虑了一类带导数项的ginzburg ? landau方程，通过构造一些类似于发展方程守恒律的泛函及巧妙的积分估计，证明了当粘性系数趋于零时， ginzburg ? landau方程的解逼近相应的带导数项的schr ( ? ) dinger方程的解，并给出了最优收敛速度估计；在二维情形，我们证明了一类带导数项的广义ginzburg ? landau方程整体光滑解的存在性，以及在某种特殊情形下， gl方程的解趋近于相应的带导数项的schr ( ? ) dinger方程的弱解；在一般情形下，我们讨论了一类ginzburg ? landau方程的非齐次边值问题，通过几个积分恒等式，同时估计解的h ~ 1模及法向导数在边界上的模，证明了整体弱解的存在性。