normal derivative meaning in Chinese
法向导数
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。 - Finally a set of equations with initiate values for boundary value problem is established where the velocity potential and its normal derivative are unknowns . because the model includes the effects of both the time and space to the velocity potential of free surface , it can be applied to strong nonlinear wave . as examples , solitary wave is computed in the numerical flume
推导给出计算域内以所有节点波势函数和波面位置高度的时间增量为未知量的线性方程组，并同时考虑时间因素和空间变位对波面势函数的影响，在预设的计算精度下，通过时步内的循环迭代逐一确定每个时步上的波面运动位置，从而建立了一种可适于求解强非线性波浪变形计算的数值模式。